Options — the whole chapter in plain English

Why options exist at all

Chapter 3 left you with futures: a commitment to buy or sell, with a linear payoff — unlimited profits and unlimited losses on both sides.

Some participants want something different. They want to ride the upside but restrict the downside. That is the entire reason options were invented, and the workbook says so in exactly those words.

The definition, one sentence at a time

An option is a contract that gives the holder the right, but not an obligation, to buy or sell the underlying asset on or before a stated date/day, at a predetermined price.

That right is bought for a price — the option premium.

• The party taking a long position (buying the option) is the buyer or holder.
• The party taking a short position (selling the option) is the seller or writer.
• The option buyer must pay the premium to the option seller upfront — at the time of buying.

Now the asymmetry that runs through this entire chapter:

The buyer has the right but no obligation. The writer has the obligation but no right.

So the buyer exercises only when the situation is favourable to him, and the writer is legally bound to honour the contract whenever the buyer decides to exercise.

Two types:

• A call option gives the buyer the right to buy the underlying.
• A put option gives the buyer the right to sell the underlying.

The two quotes the chapter is built on

The workbook uses one call and one put, both on Nifty, both strike 18400, both expiring 25 May 20XX, quoted on 10 May 20XX with the underlying at 18315.10.

Hold on to these two numbers — 124.50 and 177.60 — because the chapter dissects them later.

The vocabulary

Index option — the underlying is a stock index, such as Nifty or Sensex. Stock option — the underlying is an individual stock, such as ONGC or NTPC.

Buyer of an option — has a right but not the obligation, and pays the option premium for it. The right to buy in a call, the right to sell in a put.

Writer of an option — receives the premium and is thereby obliged to sell or buy if the buyer exercises. He has a sell obligation in a call (when the call holder exercises his right to buy) and a buy obligation in a put (when the put holder exercises his right to sell).

American option — the holder can exercise at any time on or before the expiry date. European option — the holder can exercise only on the expiry date.

In India, all index and stock options are European style options. Memorise that line; it is asked directly.

Option premium — the price the buyer pays the seller. In the example, ₹124.50 for the call and ₹177.60 for the put. These are per unit — to get the total premium for the contract you must multiply by the lot size.

Spot price (S) — the price of the underlying in the spot market: 18,315.10 here.

Strike price / exercise price (X) — the price per share at which the underlying may be purchased by the call holder or sold by the put holder: 18400 for both.

Open interest — as in futures, the total number of option contracts outstanding for an underlying.

Exercise of options — since Indian exchange-traded options are European, buyers can exercise only at maturity, and all such options are exercised with respect to the settlement value / closing price of the stock on the day of exercise.

Assignment of options — the allocation of exercised options to one or more option sellers.

Opening and closing option positions

Opening transaction — adds to or creates a new position. Either:

• Opening purchase (long on option) — the purchaser intends to create or increase a long position in a given series of options.
• Opening sale (short on option) — the seller intends to create or increase a short position.

Closing transaction — reduces or eliminates an existing position by an offsetting purchase or sale. Also called squaring off. Either:

• Closing purchase — reduces or eliminates a short position. Often called covering a short.
• Closing sale — reduces or eliminates a long position.

And a note that catches people out: you do not close a long call by buying a put. A closing transaction requires an option contract with the same terms — the same strike price and the same expiry date.

Contract specifications

As with futures, the exchange decides all terms and conditions except the option premium.

Contract size / lot size — the number of units of the underlying in one contract, different for different stocks and indices. With a Nifty lot size of 50, the total premium for the call in our example is 124.50 × 50 = ₹6,225, and for the put 177.60 × 50 = ₹8,880.

Contract trading cycle — index options in India are available for a wider range of expiration dates than stock options.

• Stock options on NSE follow a three-month trading cycle — near month, next month, far month.
• Index options on NSE and BSE are available with weekly as well as monthly maturities. They trade for 4 serial weekly cycles, excluding the monthly near-, mid- and far-month expiries. On 10 May 2023 you had weekly Nifty options expiring 11 May, 18 May, 1 June and 8 June, plus monthly contracts expiring 25 May, 29 June and 27 July.
• Index options also carry three quarterly expiries (March, June, September, December cycle).
• Exchanges also offer long-term index options with 8 half-yearly expiries on the June–December cycle, after the three quarterly expiries.

Expiration date — the last trading day of the contract. Nifty and Bank Nifty options expire on the last Tuesday of the expiry month, or the previous trading day if that Tuesday is a trading holiday. BSE and NSE decide the expiry day for their various indices, subject to change after due notice.

As per the SEBI circular dated 1 October 2024, exchanges may provide derivatives contracts with weekly expiry for only ONE of their benchmark indices — effective 20 November 2024. So BSE can offer a weekly index derivative on either Sensex 30 or Bankex, not both; NSE likewise on only one index.

Tick size — the minimum move allowed in the price quotation. For index contracts it is 5 paisa. For stock contracts it varies:

The workbook notes why it matters: a small tick size allows better risk management because positions can be adjusted on small price movements, while a large tick size may require higher margins because of the potential for larger price fluctuations.

Final settlement price. Two things here, and both are tested. Unlike futures contracts, there is no daily settlement of options contracts. And because all exchange-traded index and stock options in India are European, exercise and assignment are permitted only on the expiration date. The final settlement price is the closing price of the relevant index or stock in the cash segment on the last trading day.

Trading hours — 9.15 a.m. to 3.30 p.m., Monday to Friday.

BSE Sensex options differ slightly:

Moneyness — three states, two directions

ITM would give the holder a positive cash flow if exercised immediately. ATM would give zero. OTM would give a negative cash flow — the strike is worse than the spot for the holder.

In practice strike prices sit at fixed intervals of ₹5, ₹10 or ₹50 while the spot moves in much smaller increments, so the two are rarely exactly equal. So an ATM option is defined as the option whose strike is closest to the spot price. With the index at 18415 and strikes of 18350, 18400 and 18450 available, the 18400 strike is ATM.

Apply it to the chapter's own quotes, with spot at 18315.10 and strike 18400: the put is in-the-money and the call is out-of-the-money.

Intrinsic value and time value

Option premium = intrinsic value + time value.

Intrinsic value is the amount by which the option is in-the-money — what the buyer would realise, before adjusting for the premium paid, if he exercised instantly.

• Call: intrinsic value = S − X, minimum zero
• Put: intrinsic value = X − S, minimum zero

Only in-the-money options have intrinsic value. ATM and OTM options have zero intrinsic value. And intrinsic value can never be negative, because an option holder is not bound to exercise an option if doing so would give him a loss.

Time value = premium − intrinsic value. ATM and OTM options have only time value.

Back to the two quotes:

The four payoff positions

A long option position has limited risk (the premium paid) and unlimited profit potential. A short option position has unlimited downside risk but limited upside (the premium received).

When you are long an equity option: you have the right to exercise, your potential loss is limited to the premium paid, and profit depends on the underlying price at exercise or expiry.

When you are short: your maximum profit is the premium received, you can be assigned an exercised option any time during the life of the contract in the case of American options — and all option writers should be aware that assignment is a distinct possibility — and your potential loss is theoretically unlimited.

Long call

Index at 17562. You buy a near-month call, strike 17500, premium ₹95.

If the index closes at 17400 you will not exercise — why buy at 17500 what the market sells at 17400? You let it lapse and your loss is the ₹95 premium.

Because the underlying is an index and cannot conveniently be bought or sold on expiry day, long positions in index options are cash-settled on the expiration date: an ITM call holder receives the difference between the strike price and the closing spot value of the index.

At 17595 you receive a payoff of ₹95, which exactly offsets the ₹95 premium — net gain zero. That is the break-even point.

BEP for a call = strike price + premium (X + P).

At 18000 the payoff is 500, less the ₹95 premium, so profit is ₹405.

With a lot size of 50, contract value is 17500 × 50 = ₹8,75,000 and the maximum loss is 95 × 50 = ₹4,750. So: loss limited to ₹4,750, profit potentially unlimited.

Note also where losses begin to shrink — as soon as the index rises above 17500, not at the BEP. Above 17500 the option has intrinsic value; above 17595 it has more than the premium.

And a rule the exam loves: a call option buyer pays NO margin to the exchange. His payment obligation is restricted to the premium already paid, he can suffer no further loss, so no margin is required.

Short call

Every buyer has a seller, so the short call is the exact mirror image.

Maximum gain = premium received (₹95), as long as the index stays below the strike. Maximum loss = unlimited.

BEP for a short call is also X + P. The workbook states the principle: BEP is independent of position (long or short); it is instrument specific.

The call seller must pay a margin to the exchange, because he has an obligation, his losses can be unlimited, and he is therefore a potential risk to the stability of the system.

Long put

Buy a near-month put, strike 17500, premium ₹150. You hold the right to sell the index at 17500, and you will do so only when the index is below 17500.

Maximum loss is the ₹150 premium. Maximum profit occurs if the index falls to zero — profit ₹17,500 less the ₹150 premium = ₹17,350.

BEP for a put = strike price − premium (X − P) = 17350 here.

Maximum loss = 150 × 50 = ₹7,500; contract value 17500 × 50 = ₹8,75,000. Losses start reducing as the index dips below 17500, and profits begin below 17350.

The put buyer pays no margin either. The workbook gives the general rule: a margin is paid only if there is an obligation, and an option buyer — of a call or a put — has no obligation.

Short put

The mirror of the long put.

Gain fixed at the ₹150 premium; losses begin below the BEP of 17350. The put seller pays a margin because he has an obligation to take delivery and his losses can be huge.

Futures versus options

Options have asymmetric risk exposure — the gain when the underlying moves one way is significantly different from the loss when it moves the other. Futures have symmetric risk exposure.

Leverage. An option buyer pays a relatively small premium for market exposure in relation to the contract value. ₹4,750 for the long call and ₹7,500 for the long put, on a contract value of ₹8,75,000 in both cases. Small favourable moves in the underlying produce large percentage gains.

But leverage cuts both ways. If the underlying does not move as anticipated, leverage magnifies the percentage loss, and if the options expire with no value, the entire premium is lost.

What determines the option premium

Not the exchange, and not SEBI. Prices are never fixed by stock exchanges or SEBI. Price discovery is a critical and basic component of markets — exchanges only provide a platform, and SEBI's role is to ensure smooth functioning.

Five fundamental parameters:

1. Spot price of the underlying asset
2. Strike price of the option
3. Volatility of the underlying asset's price
4. Time to expiration
5. Interest rates

Spot price. If the underlying rises, call value increases and put value decreases. If it falls, call value decreases and put value increases.

Strike price. With everything else constant, an increase in the strike price decreases the intrinsic value and hence the value of a call. So with the index at 17562, a 17600 call trades higher than a 17700 call. The reverse holds for puts: an increase in strike increases put value, so a 17700 put trades at a higher premium than a 17600 put.

Volatility. The magnitude of movement in the underlying, up or down. It affects calls and puts in the same way. Higher volatility means a higher premium, because there is a greater possibility the option moves in-the-money during the contract's life. When volatility shoots up on some unexpected event, the prices of both calls and puts rise.

Higher volatility = higher premium. Lower volatility = lower premium. For both calls and puts.

Time to expiration. Works like volatility. Longer maturity means greater uncertainty and hence a higher premium — a three-month 17500 option generally trades above a one-month 17500 option. And with all else equal, the time value falls with the passage of time. This is time decay, and it is why options are known as "wasting assets".

Then the workbook draws a conclusion candidates often miss. Of the two components, time value is inherently biased towards reducing in value. So if all things remain constant through the contract period, the option price will always fall by expiry — which means option sellers are at a fundamental advantage compared with option buyers, because there is an inherent tendency in the price to go down.

Interest rates. These are more complicated and affect different options differently — the impact is greater on options on individual stocks and indices than on options on futures. Simply put: high interest rates increase the value of a call and decrease the value of a put.

The Greeks

Option premiums change with the factors that determine option pricing. The sensitivities tracked in the market are collectively the Greeks: Delta, Gamma, Theta, Vega and Rho.

Delta (δ or ∆) — the most important of the Greeks. It measures the sensitivity of the option value to a small change in the price of the underlying, and can be read as the speed with which an option moves with respect to the underlying price.

Delta = change in option premium ÷ unit change in price of the underlying

A call delta of 0.60 means a ₹1 change in the underlying moves the call price by 60 paise.

Delta matters because it is heavily used in margining and risk management, and it is often called the hedge ratio. If you hold n shares of a stock, then n divided by the delta gives the number of calls you would need to write to create a hedge. In such a delta neutral portfolio, a gain on the shares from a rise in price is exactly offset by the loss on the calls written, and vice versa.

Gamma (γ) — the change in delta for a unit change in the price of the underlying. It is the second derivative of the option price with respect to the underlying price.

Gamma = change in option delta ÷ unit change in price of underlying

Gamma works as the acceleration of the delta — the speed with which an option will go either in-the-money or out-of-the-money because of a price change. A call with delta 0.50 and gamma 0.08: a ₹1 rise in the stock changes the delta by 0.08, so the new delta is 0.58.

Theta (θ) — sensitivity to time decay: the change in option price given a one-day decrease in time to expiration.

Theta = change in option premium ÷ change in time to expiry

A call with 5 days to expiry and theta of 1.2 loses ₹1.20 for each day until expiry. Theta is usually negative for a long option, whether call or put — other things equal, options tend to lose time value each day throughout their life.

Vega (ν) — sensitivity to changes in market volatility: the change in premium for a given change (typically 1%) in the underlying volatility.

Vega = change in option premium ÷ change in volatility

A call with vega 0.80 changes in premium by 0.80% for every 1% change in the implied volatility. Vega is positive for a long call and a long put — more assumed volatility increases the expected reward from any long option position.

Rho (ρ) — the change in option price for a one percentage point change in the risk-free interest rate. It measures the change in the option's price per unit increase in the cost of funding the underlying.

Rho = change in option premium ÷ change in cost of funding the underlying

Option pricing models

The Binomial Pricing Model — developed by William Sharpe in 1978. It represents the price evolution of the underlying as a binomial tree of all possible prices at equally spaced time steps, assuming that at each step the price can only move up or down at fixed rates with simulated probabilities. It is the most flexible, intuitive and popular approach, and very accurate because it is iterative — but its implementation is complex and time consuming.

The Black & Scholes Model — published in 1973 by Fisher Black and Myron Scholes. Popular, relatively simple and fast, and unlike the binomial model it does not rely on calculation by iteration. It computes a theoretical call price (ignoring dividends paid during the life of the option) from the five key determinants: stock price, strike price, volatility, time to expiration and the short-term risk-free interest rate.

C = SN(d1) − Xe^(−rt)N(d2) P = Xe^(−rt)N(−d2) − SN(−d1)

with S the stock price, X the strike price, t the time remaining until expiration in years, r the current continuously compounded risk-free interest rate, v the annual volatility of the stock price (the standard deviation of short-term returns over one year), ln the natural logarithm, N(x) the standard normal cumulative distribution function and e the exponential function.

Implied volatility

Volatility is one of the most important drivers of an option price — and volatility is invisible. So how is it measured?

Historical volatility takes percentage price changes in the underlying over a past period: for instance, the weekly percentage changes in Nifty over the past one year, and the standard deviation of those changes.

But option traders do not use just historical volatility. What they want is how volatile the stock is expected to be over the remaining life of the option.

The workbook's illustration: a pharmaceutical company's stock has been range-bound for a year with historical volatility around 15%. It is fighting an important court case with a verdict due next week — a favourable outcome boosts sales and profits of its most important product, an unfavourable one causes huge losses. The expected volatility over the next week could be as high as 70% or 80%.

Implied volatility is found by running the Black-Scholes model in reverse. If the index is at 17562, a 17500 call with 9 days to expiry trades at ₹95, and the interest rate is 6%, then every input is known except volatility — so you solve for the volatility that produces a price of ₹95. It is different from historical volatility because it is worked out from the option price rather than from the historical price movement of the asset.

How traders use it: when implied volatility is high, option traders start selling options. When implied volatility is low, traders like to buy options. With implied volatility at 80% the day before the verdict, the option price itself is very high, so traders would sell.

And the workbook adds the writer's logic: because they are at the receiving end of the asymmetric nature of option payoffs, writers tend to extract higher premiums from buyers, which works as a margin of safety for them. If put writers had already factored an adverse verdict into their pricing, even an adverse verdict may not really lead to losses for them — they collected a high premium precisely for that eventuality. The same applies to call writers on a favourable verdict.

Choosing a strike: buyer's and seller's perspectives

If an option is deeply in-the-money, its intrinsic value is high and so is its premium. ATM and OTM options have no intrinsic value, only time value, so they are cheaper. Hence an option buyer pays a higher premium for an ITM option than for an ATM or OTM option.

For ATM options the uncertainty is highest. An ITM or OTM option that moves somewhat still stays largely ITM or OTM. But a small price movement in either direction can tip an ATM option from ATM to ITM or OTM. That uncertainty is a function of time to expiry and volatility, both of which are captured in the time value.

Call buyer's analysis

Index at 17562. Four calls:

The 17300 call is deep ITM with intrinsic value 17562 − 17300 = 262, so its premium is at least that much; the remaining 327 − 262 = 65 is time value. The 17600 call is OTM — no intrinsic value, the entire ₹130 is time value.

If the index closes below 17300 all four expire worthless. The greatest loss is on the 17300 strike (₹327 premium) and the least loss on the 17600 strike (₹130).

Return on investment is where the choice becomes interesting. ROI = net profit as a percentage of the premium paid. If the index rises to 17800:

Note that the highest rupee profit and the highest ROI are on different strikes.

Call seller's analysis

A call option seller has a neutral to bearish perspective. He makes a fixed gain equal to the premium received when the index closes below the strike; his gain reduces and turns into losses as the index closes higher.

Put buyer's analysis

Index at 17562. Four puts:

The 17600 put is ITM — intrinsic value 17600 − 17562 = 38, and 167 − 38 = 129 is time value. The 17300 put is OTM; for the other strikes the entire premium is time value. Notice the pricing logic: the ITM 17600 strike commands ₹167 while the OTM 17300 strike sells at just ₹65.

If the index falls to 17000:

Generally the buyer of a deep OTM put gets a higher return on investment if the price of the index falls drastically — the highest rupee profit is on the ITM strike, but the highest percentage return is on the cheapest, most out-of-the-money one.

Put seller's analysis

A put option seller has a neutral to bullish perspective. And the workbook's conclusion is worth quoting: the seller of put options incurs higher risk in selling deep ITM put options even though they fetch higher returns in terms of option premiums. Selling deep OTM put options is less risky but comes with lower premium.

The trader's real choice, then, is across futures of various expiries and options of various expiries and strikes — and which combination he picks depends on his analysis of market conditions and his risk appetite. That is what Chapter 5 builds on.