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risky2018
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Joined: June 29th, 2018, 8:23 am

FX Realised Vol knock outs

June 29th, 2018, 8:29 am

 Hi, could someone tell me how do people hedge realized vol knock out ?
For example this could be a European digital call where the option could knock out at expiration if the realized vol is above the barrier. Thanks.
 
frolloos
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Location: Netherlands

Re: FX Realised Vol knock outs

June 29th, 2018, 9:52 am

Is this a KO where the underlying is the realised vol/variance of an FX pair, or is this a FX option contingent on the realized var/vol?
 
risky2018
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Joined: June 29th, 2018, 8:23 am

Re: FX Realised Vol knock outs

June 29th, 2018, 9:58 am

Digital call option on FX and the KO at expiration is dependent on the realized vol of the same FX pair. I think on the sell side, traders will hedge with risk with vanilla options and forwards.
 
frolloos
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Location: Netherlands

Re: FX Realised Vol knock outs

June 29th, 2018, 11:12 am

Since the knockout is only at expiration then the payoff of the option can be written as

[$] \theta (X_T - K) \theta (L - V_T) [$]

where [$] \theta [$] is the Heaviside function, [$] X_T [$] is exchange rate at maturity, [$] V_T [$] is the realised variance at maturity, and [$] K, L [$] are the strikes. Agree? 

Let's assume first that the realised variance and exchange rate are independent. The price of the option is then

[$] E_t [\theta (X_T - K)] E_t [\theta (L - V_T)] [$]

which is. the product of two digital options. Hence, to hedge the total option you'll need to hedge using both FX forwards and variance swaps, or alternatively dynamically rebalance a vanilla FX digital by an amount equal to the vanilla FX variance / vol digital (if those are traded at all).

In the case where the correlation is non-zero you'll have a bit more work to do.

Hope this helps.
 
risky2018
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Joined: June 29th, 2018, 8:23 am

Re: FX Realised Vol knock outs

June 30th, 2018, 4:44 am

Yes agree. Suppose if the traders do not want to buy vol swaps (lower liquidity), how can a vol swap be replicated using vanilla options in general ? Thanks. 
 
frolloos
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Location: Netherlands

Re: FX Realised Vol knock outs

June 30th, 2018, 6:53 am

Do you mean volswaps or varswaps? You don't need volswaps. Varswaps will do as well for this particular problem. And the liquidity of varswaps is not necessarily less than the strip of vanilla options replicating the varswap.
 
risky2018
Topic Author
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Joined: June 29th, 2018, 8:23 am

Re: FX Realised Vol knock outs

June 30th, 2018, 10:48 am

just curious what would be the difference between using vol swaps vs var swap for this problem ?
 
frolloos
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Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

Re: FX Realised Vol knock outs

June 30th, 2018, 11:19 am

I think there is less liquidity in volswaps, at least in equity derivatives. The situation might be different in FX space, although I doubt it. However there are ways to replicate volswaps and they are traded as well of course.