I would like to share this book just published on amazon
Cracking the Finance Quant Interview: 51 Interview Questions and Solutions
You can preview brainteasers with the "look inside" button on amazon. I will add a few questions here
Two sided corridor with rates:
Let Bt be a Brownian Motion and u and d two positive real numbers. We consider an option which pays 1 if Bt reaches u and remained greater then−d since inception
∃ t0 : Bt0=u ; ∀ t ∈ [0,t0] , Bt>−d
payment is made when the barrier is touched. Calculate the price of this option with rates r >0.
The binary hedge:
A trader suggests the following binary hedging strategy for a call option:
•sell a call option at strike K > S0
•buy the stock at K when St is increasing and crosses K
•sell the stock at K when St is decreasing and crosses K
What is wrong with this strategy?
End of times:
Let Xn be a sequence of positive random variables, such that E[Xn] =a and
limn→+∞Xn= 0 a.s
show that limn→+∞E|Xn−K|=a+K
Can this result be applied to a financial option?