Exchange Traded Interest Rate Options

Chapter 4: Exchange Traded Interest Rate Options

NISM Series IV — Interest Rate Derivatives | ~8% weightage | ~32 questions

What this chapter is about

Options on interest rate instruments — same framework as Series VIII equity options but with bond prices as the underlying. Call options, put options, Greeks, breakeven, P&L calculations. Heavy overlap with Series I (Currency) CH4. The new addition for IRD: option P&L calculations involving bond prices as the underlying, and the short straddle/strangle strategies.

Key concepts — same as other option modules

Call option: Right to BUY the underlying bond at the strike price.

• Buyer is bullish on bond (expects bond price to RISE = expects rates to fall)
• Buyer pays premium, has unlimited profit potential, limited loss (= premium paid)

Put option: Right to SELL the underlying bond at the strike price.

• Buyer is bearish on bond (expects bond price to FALL = expects rates to rise)
• Buyer pays premium, has unlimited profit potential, limited loss (= premium paid)

Only European style options on Indian exchanges.

Premium settlement: Cash settled (upfront by buyer to seller).

Option expiry for interest rate options: Last Thursday of the month.

Option payoff calculations — heavily tested

Long Call:

• Payoff = max(Bond price at expiry − Strike, 0)
• Net payoff = max(Bond price − Strike, 0) − Premium paid
• Breakeven = Strike + Premium paid

Long Put:

• Payoff = max(Strike − Bond price at expiry, 0)
• Net payoff = max(Strike − Bond price, 0) − Premium paid
• Breakeven = Strike − Premium paid

Short Call (sold call):

• Net payoff = Premium received − max(Bond price − Strike, 0)
• Breakeven = Strike + Premium received

Short Put (sold put):

• Net payoff = Premium received − max(Strike − Bond price, 0)
• Breakeven = Strike − Premium received

Complex P&L examples — exam favourites

Example 1: Buy Rs 21.50 call at Rs 0.20 premium. Bond closes at Rs 21.70.

• Payoff = 21.70 − 21.50 = 0.20
• Net = 0.20 − 0.20 (premium) = Rs 0 (breakeven)

Example 2: Sell Rs 40.50 put at Rs 0.35 premium. Bond at Rs 40.50 at expiry.

• Put is at-the-money → expires worthless
• Net = Rs 0.35 premium received (full profit)

Example 3: Buy Rs 21.50 call (Rs 0.20 premium) + sell Rs 39.50 call (Rs 0.60 premium). Underlying = Rs 39.50 at expiry.

• Long call 21.50: in-the-money but... wait this is different strikes on different underlyings
• Short call 39.50: spot = strike = at-the-money → expires worthless → keep Rs 0.60
• Net premium = 0.60 − 0.20 = Rs 0.40 profit

Example 4 (Covered call): Buy bond at Rs 54.50, sell Rs 55 call at Rs 0.10. Bond = Rs 55.50 at expiry.

• Bond gain = 55.50 − 54.50 = Rs 1.00
• Call loss = (55.50 − 55) = Rs 0.50 (called away)
• Premium received = Rs 0.10
• Net = 1.00 − 0.50 + 0.10 = Rs 0.60

Example 5 (Long straddle): Buy call Rs 150 (Rs 0.30) + buy put Rs 150 (Rs 0.20). Bond = Rs 149.50.

• Call expires worthless (OTM)
• Put payoff = 150 − 149.50 = Rs 0.50
• Total premium paid = 0.30 + 0.20 = Rs 0.50
• Net = 0.50 − 0.50 = Rs 0 (breakeven)

Option Greeks

Delta: Rate of change of option price per unit change in underlying. Used for hedging.

Theta: Measures TIME DECAY. Negative for option buyers — premium falls as expiry approaches. Time value of option is directly proportional to time to expiry.

Gamma: Rate of change of Delta. Second-order measure.

Vega: Sensitivity to volatility. Higher volatility → higher premium for both calls and puts.

Rho: Sensitivity to interest rates.

Historical volatility: Calculated from past closing prices. Implied volatility: Derived from current option prices. Rise in implied volatility = advantageous for BOTH call buyers and put buyers.

Key pricing factors

| Factor | Call premium | Put premium | |--------|-------------|------------| | Bond price rises | Increases | Decreases | | Volatility rises | Increases | Increases | | Time to expiry increases | Increases | Increases | | Strike price increases | Decreases | Increases |

Option strategies

Short straddle: Sell both call and put at SAME strike. Profit from low volatility. Short strangle: Sell call at higher strike + sell put at lower strike (both OTM). Profit from low volatility. Bull call spread (bullish vertical): Buy lower strike call + sell higher strike call. Bull put spread (bullish vertical using puts): Buy lower strike put + sell higher strike put. Butterfly: Long call at lower strike + long call at higher strike + 2 short calls at middle strike.

Butterfly P&L example:

• Long 125.50 call (Rs 0.60) + Long 126.50 call (Rs 0.20) + 2 Short 126.00 calls (Rs 0.30 each)
• At expiry = Rs 127: payoffs 1.50 − 2.00 + 0.50 = 0
• Net premium paid = 0.60 + 0.20 − 0.60 = Rs 0.20
• Net P&L = 0 − 0.20 = Loss of Rs 0.20

Trap Alert

Trap 1: "Theta is positive for option buyers" — FALSE Theta is negative for buyers (time decay erodes premium). Positive for sellers.

Trap 2: "Rising volatility only benefits call buyers" — FALSE Rising volatility increases premium for BOTH calls and puts. Benefits all option buyers.

Trap 3: "Option value = Intrinsic value × Time value" — FALSE Option value = Intrinsic value + Time value (ADDITION, not multiplication)

Trap 4: "Interest rate options expiry = Last Wednesday" — FALSE IRD options expiry = Last Thursday (same as G-Sec bond futures, unlike T-bill futures which is Wednesday)

Must-remember rules

• European options only on Indian exchanges
• Option premium = Intrinsic value + Time value (always)
• Intrinsic value = never negative (minimum zero)
• Breakeven call buyer = Strike + Premium | Put buyer = Strike − Premium
• Time value directly proportional to time to expiry (more time = more time value)
• Theta = time decay (negative for buyers)
• Volatility rise = premium rise for both C and P
• Historical volatility = based on past closing prices
• Implied volatility = derived from current option prices
• Option expiry for IRD = Last Thursday of month
• Short straddle/strangle = profit from low volatility
• Bull call spread = buy lower strike call + sell higher strike call

Quick revision — 60 second scan

• European options only | Premium = Intrinsic + Time (additive, never negative)
• Breakeven: Call = S + P | Put = S − P
• Higher volatility → higher premium (both C and P)
• Theta = time decay | Vega = volatility sensitivity
• Long call: buy bond call, bullish (rate fall) | Long put: buy bond put, bearish (rate rise)
• Historical vol = past prices | Implied vol = from current option prices
• IRD option expiry = Last Thursday
• Short straddle = both options sold, same strike, profit from stability