Options Arbitrage

[Eubie 10]

Hello guys,

 

I tried to find a forum dedicated to financial derivates pricing without success, so Im trying my luck here. My question is only partially related to trading, altough it is dependent on the no arbitrage condition. So...

 

I have two currency call options, let's say CHF/USD and CHF/EUR (meaning I can buy USD and EUR for CHF). Consider that CHF/USD is not exanchange traded but I still want to deduce it's price. Hence, I create a strategy, starting with 100 CHF.

 

I do the following:

1/ get the option premium P1 of a call on CHF/EUR with strike S1

2/ buy 100/P1 calls with strike S1

3/ calc the NPV of holding these options till maturity. The cashflow per one call is (-P1 + max( S[TTM] - S1, 0 )* discountFactor) where discountFactor si the usual exp(-swissRiskFreeRate * TTM) and S[TTM] can be approximated from forward curves.

4/ Sum up the cashflows for all 100/P1 options bought.

 

Hence I have a cashflows from investing 100 CHF into CHF/EUR options.

 

Now, if I want to invest my 100 CHF into CHF/USD calls and do the same calculations with a unknown premium P2 of the CHF/USD, I end up with the cashflow from investing into CHF/USD options. By equating these two cashflows I can get the theoretical premium P2. And the question is whether this approach to getting the premium P2 is valid. I can't find any bug in it but I would like to know the opinions of others.

 

Any input is much appreciated.

Daniel