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I'm trying to price a European call option on USDJPY. We have that $S = 112.79, K = 112.24, \sigma = 6.887\%, r_d = 1.422\%, r_f = -0.519\%, T = 0.25$. My model, based on Black-Scholes, returns the value $c = 2.149$.

Additionally, the price of the put is $p = 1.055$ and put-call parity holds. I'm confident that my model is correct. However, Bloomberg, which also uses the Black-Scholes model, returns the result (for $1M notional) as 121.107 pips or 1.3594%P.

How do I get from my value $c$ to a value roughly the same as the one generated in Bloomberg?

Edit: Do I just divide my formula result by $S$?

TIA!

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  • $\begingroup$ I'm no expert in FX, but 112.79 is the price of a dollar paid in yen, so shouldn't the "domestic" interest be the yen interest rate (negative) and the foreign the (positive) US rate? $\endgroup$ – noob2 Jan 9 '18 at 20:46
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For USDJPY the convention is considered to be buying dollar, selling yen so the foreign rate (one we are buying into) would be the dollar and the domestic (what we are paying) is yen. Pricing on these values returns roughly C = 121 USD pips, ~13K USD on $1M notional

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