Calculating vega for IRS

[Abhinav Agrawal]

I am a bit confused if someone asks you how do you calculate vega for Interest Rate Swap. From my understanding, volatility or Implied Volatility is what can be derived from current market price. So for option pricing, you can calculate how market price varies with change in volatility (Black Scholes,etc). However for IRS, we calculate market price by discounting cashflows, how does volatility come into the picture here?

 

[Abhinav Agrawal]

Is it calculated using GARCH? So from the historical interest rates, we can calculate the long run volatility of interest rates and the new volatility figure is plus 1 bps (if you want to measure vega of IRS). Back calculating, can we get the return due to the volatility change from the GARCH(1,1) model?

 

[aadityafrm]

Per my understanding, measure of Vega is applicable only for portfolio which would contain swaptions and not for IRS. Here, implied volatility is derived from option value on interest rate swaps. However, IRS would have delta and gamma (convexity) measures for any type.

 

[Abhinav Agrawal]

I work with an investment bank and I do see the vega for IRS, hence the question.

 

[ashanks]

Here's my understanding:

Volatility is not always implied volatility. You could historically measure 'realized volatility' - of returns, of interest rates of any parameter.

So to answer your question, you can numerically estimate vega for a IRS by bumping the volatility (input) used in the model for pricing the IRS, and seeing the change in price. This is similar to what you're describing in your second post using GARCH. The specifics would depend on the model.

 

[ShaktiRathore]

hi
you can apply if possible BSm model,
replace stock price with interest rate i and the fixed rate as the exercise price. The term of the swap as the maturity of the option and apply the formula for simple option vega to arrive at the vega of the IRS. For IRS receive floating and pay fixed will be treated as a call option on interest rate whose payoff is positive when interest rate exceeds fixed rate(exercise price) calculate vega for this similar to vega of call option.similarly for IRS receive fixed and pay floating will be treated as a put option on interest rate whose payoff is positive when interest rate fall below fixed rate(exercise price) calculate vega for this similar to vega of put option.
i would also give a different perspective,
vega for IRS can be defines as change in IRS value/change in value of volatility of underlying which is interest rate
mathematically, its vega(IRS)= d(IRS value)/d(volatility of interest rate)
assuming fixed for floating IRS,
IRS value=NP*period*(fixed rate-floating rate)
differentiating wrt volatility of interest rate,
d(IRS value)/d(volatility of interest rate)
=d[NP*period*(fixed rate-floating rate)]/d(volatility of interest rate)
=NP*period*d(fixed rate-floating rate)]/d(volatility of interest rate)
=NP*period*d(0-floating rate)]/d(volatility of interest rate)
=-NP*period*d(floating rate)/d(volatility of interest rate)
so vega of IRS is proportional to the change in interest rate typically libor w.r.t the volatility of the interest rate
interest rate volatility determines how sensitive IRS value to the volatility of the interest rates
thanks

 

[cfrm17]

There is Gamma but no Vega in interest rate swaps as the pricing model doesn't take volatility.