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NISM Series XIII module
Chapter reading
S4_CH4
Workbook pages 120-145
Concept lesson
This is the learning layer for Exchange Traded Interest Rate Options: bond math, yield logic, formulas, delivery rules, traps and quick revision. The practice buttons sit on the side only after the concept has landed.
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.
**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.
**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
**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)**
**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.
| 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 |
**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 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)