Abstract
We develop a new framework of foreign exchange (FX) options pricing under intervention and incorporate the effect of intervention by assuming a FX rate process which is stopped by a hitting time of an absorption boundary. More importantly, the proposed model satisfies the arbitrage-free condition. We derive closed-form pricing formulas for European and digital put options, and Greeks of a European put option. We show numerical examples for the case of the EUR/CHF options in the market, where the Swiss National Bank has been intervening since September 2011. We investigate how the present values of the options differ under intervention by comparing the model's prices with those of the market. We observe that the model indicates significantly lower present values than the market prices for the options which have a payoff in a low strike area.
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