[R-SIG-Finance] [R-sig-finance] Domestic risk free rate in FX option
kriskumar at earthlink.net
Tue May 12 03:04:35 CEST 2009
To add my two cents to this.. Black-76 formula is really Black-scholes with the substitution F=S*exp((r-q)T) and is the formula used to price options in currency land on options on forwards in general. The black-76 formula gives you a value in term pips so in the case of EURGBP the value that comes out of the formula is in GBP pips. In order to convert this as a % of EUR notional you divide by Spot. If you are dealing with a GBP notional then you divide the result from the formula by strike to get this as a % of GBP notional. Typical quoting convention is to quote as a % of BASE (EUR) notional.
In general it is useful to think of the equivalence to stocks when IBM is quoted as 102$ it is really IBMUSD => the amount of USD you need for one unit of IBM. So here IBM is the base or foreign ASSET and USD is the TERM or domestic asset in whose units the price is quoted. So when you price an option on IBM the value you get is in term (USD) units
Hope this helps,
>From: Mahesh Krishnan <heshriti at gmail.com>
>Sent: May 10, 2009 9:53 PM
>To: RON70 <ron_michael70 at yahoo.com>
>Cc: r-sig-finance at stat.math.ethz.ch
>Subject: Re: [R-SIG-Finance] [R-sig-finance] Domestic risk free rate in FX option
>Ultimately, currency options calculations depend on what you take as
>numeraire- the domestic currency, and what you take as the foreign currency.
>In the case of CME, EUR/GBP is quoted as pounds per euro, i.e. the domestic
>currency is pounds and foreign currency is euro.
>So if you were to price options on currencies using standard Merton's stock
>formula, you use the risk free rate of UK as domestic, and risk free rate of
>Euro zone as your "dividend yield".
>To my knowledge, CME only has options on futures, not spot currency. And if
>you are trying to price that, you basically plug in the risk free rate of UK
>in the futures-options model, and you get the option premium in pounds. You
>need to verify that CME option price is quoted it in pounds, I beleive it
>On Wed, May 6, 2009 at 1:12 AM, RON70 <ron_michael70 at yahoo.com> wrote:
>> In CME, option on forex is traded on EUR/GBP. If I want to price this
>> using some pricing formula then as Domestic risk free interest rate what
>> should I take? Shouldn't risk free rate in UK be appropriate? I am asking
>> this because as CME is in US, domestic currency is USD. Your suggestion
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>Mahesh Krishnan, Ph.D
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