So here are some exam questions, anybody would like to have a shot at this?1. Why do we need characteristic functions in option pricing theory?2. Assume you are interested in spread call options with payoff max(S1T−S2T−K,0) where SiT are stock indices. What approach would you suggest to come up with a price for such an option?3. Jumps and stochastic volatility are features that have similar effects on option prices. Discuss.4. The VIX index and the fixed leg of a variance swap with 30-days to maturity are identical. Discuss under what conditions this is true.5. You have written a call option on a stock index and want to hedge the risk exposure. What can you do? How does your answer depend on whether the index exhibits jumps and/or stochastic volatility.6. You want to calculate the third moment of the risk-neutral distribution. How can you do this?

1. Denisty/Distribution one to one realtionship (unknown density)2. Same as always, risk neutral discounted expectation of the payoff, but this time we need a joint distribution for S1&S25. Static/dynamic hedging. Carr & Wu static approach, hedge the call option with a portfolio of call options, making the weight not dependent on S and T, dynamic: classical delta, but how to choose weight? H=C then all the risk from the brownian motion is eliminated, but rewriting the variance b.motion as correlation of the stock b.motion you can hedge partly the variance as well by choosing the weight with respect to the correlation: Minimum variance hedge.6. Using the payoff decomposition therom one can create cubic contracts of the log price difference from t-T. With payoff as usual . Then calculation of the skew as the third moment .... have to look up the rest

2. Two firms are related not only thru macro but also certain contagion effect.3. Sort of. The effect of SV decreases as ttm decreases but jump effect doesn't.6. Breeden-Litzenberger method, being discussed.

is this a take-home ?

Nope, an oral exam.