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I got three interview questions as follows, any idea?1. how to price American binary option? I only know the European binary option formula, use numerical methods for american options?2. what is the distrubition of t=P(S<V). S is stock price, V is some certain value, t is the first time that S<V. Is it a stopping time problem?3. FX problem, say USD/EUR has volatility vol1, EUR/JPY has volatility vol2, what is the USD/JPY volatility?Thanks,

1. use options calculator2. the first–stopping time distribution3. depends on correlations

There is no close form expression for the American binary call option? I am asking out of laziness because I can't be bother to work on it at this time of night

QuoteOriginally posted by: VassiliThere is no close form expression for the American binary call option? Isn't that just a one touch option?

Q3. fx cross vols, formula is analogous to cosine theorem?can be used to back out correlation given 3 input volsor conversely calculate imp vol of an illiquid cross given 2 liquid fx crosses, input would be the correlation between the fx pairs and their respective imp vols..

It is indeed just a one touch and there is a closed form BS solution for it

Not exactly, because the payoff date is stochastic as for any american option...