# Swaptions and their Valuation

Swaption provides option holder the option to enter into a swap.

**Payer vs. Receiver****Payer Swaption:**The holder can enter into a swap as the fixed rate payer/floating rate receiver**Receiver Swaption:**The holder can enter into a swap as the floating rate payer/fixed rate receiver.Parties who expect the need for a swap in the future and want to lock in the swap rate now are common users of swaptions.

Swaptions provide flexibility to not enter a swap or postpone swap entry for a more desirable rate.

**Interest Rate Swaptions - Payoffs and Cash Flows**The holder of a payer swaption with positive value can realize this positive value in three ways (note the swaption holder will be in a situation where the floating rate received exceeds the fixed rate paid):

- Exercise the swaption and enter into a pay fixed-receive floating interest rate swap; note that this strategy entails risk as interest rates could change and thus change the floating payment received.
- Exercise the swaption and enter another pay floating-receive fixed interest rate swap at current rates. The income and outgoing swaps will offset and the swaption holder has created an annuity for him/herself.
- The swaption holder may be able to arrange to receive a lump sum payment equal to the present value of the annuity created in approach #2.

### Value of an Interest Rate Swaption at Expiration

- Payer Swaption payoff at expiration (based on $1 notional) =

**\= Max[0,FS(0,n,m) - x] ΣB0(hj)**

FS(0,n,m) = Market rate on the underlying swap at swaption expiration.

X = The exercise rate that the payer would pay under swaption terms

B0(hj) = Present value factor for each interest payment, based on the term structure at the expiration of the swaption

Receiver Swaption payoff at expiration (based on $1 notional) =

**\= Max[0, x - FS(0,n,m)] ΣB0(hj)**

- FS(0,n,m) = Market rate on the underlying swap at swaption expiration.
- X = The exercise rate that the receiver would receive under swaption terms
- B0(hj) = Present value factor for each interest payment, based on the term structure at the expiration of the swaption

- CFA Level 2: Derivatives Part 2 – Introduction
- Introduction to Options
- Synthetic Options and Rationale
- One Period Binomial Option Pricing Model
- Call Option Price Formula
- Binomial Interest Rate Options Pricing
- Black-Scholes-Merton (BSM) Option Pricing Model
- Black-Scholes-Merton Model and the Greeks
- Dynamic Delta Hedging & Gamma Related Issues
- Estimating Volatility for Option Pricing
- Put-Call Parity for Options on Forwards
- Introduction to Swaps
- Plain Vanilla Interest Rate Swap
- Equity Swaps
- Currency Swaps
- Swap Pricing vs. Swap Valuing
- Pricing and Valuing a Plain Vanilla Interest Rate Swap
- Pricing and Valuing Currency Swaps
- Pricing and Valuing Equity Swaps
- Swaps as Theoretical Equivalents of Other Derivatives
- Swaptions and their Valuation
- Swap Credit Risk and Swap Spread
- Interest Rate Derivatives - Caps and Floors
- Credit Default Swaps (CDS)
- Credit Derivative Trading Strategies

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