Pricing Swaptions on Forward-Starting Swaps

Summary

The document explains how to price options expiring at different times on the same swap, which itself begins in the future. It applies the Black 76 swaption formula to each expiry, using the relevant option expiration as the time to expiry while keeping the underlying forward swap rate the same across the cases.

The answer says market implied volatility can differ across those expiries because it reflects expectations for realized volatility over each option’s period. It offers a concise pricing principle rather than a worked numerical example, and does not discuss other model assumptions, volatility calibration, or adjustments for market conventions.

Key ideas

• Black 76 can be applied to swaptions on a forward-starting swap.
• Use each option's own expiration time in the pricing formula.
• The forward swap rate remains the same when the underlying swap is unchanged.
• Implied volatility may vary across expiries to reflect different expected volatility periods.

Tags

# Swaption pricing


# Swaption pricing












I am trying to understand the pricing of various types of swaptions.

Suppose I have a swap that starts in 3 months time. How would I go about pricing a swaption on this swap in the following cases:

1 Month option 2 Month option 3 Month option

I know the standard theory, which seems to let me price the swaption for a 3 month option. However I can't seem to figure out how to bring in the forward starting arrangement for the 1 and 2 month option.

## Answer by dm63 (score 3, accepted)

https://quant.stackexchange.com/a/28110

The Black 76 swaption formula works for all these cases. The expiration time T= 1mo, 2mo or 3mo but the forward rate of the swap is the same in each case. The market will place different implied volatilities on these 3 options, according to the expectations of realized volatility in these 3 time periods.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.