1. In the Black-Scholes formula for a vanilla call option the probability of being in the money almost equals the delta of the option when:

   1. the volatility is very low ;
   2. the volatility is very high;
   3. the volatility is very high and the risk free rate is low;
   4. the risk free rate is very low;




2. In an arithmetic average (asian) option, is the strike price and only one fixing is left out of a total of fixings. If is the average value of the underlying (spot) of all fixings until that point (here ) then the value of the asian option is equal to:

   1. times the value of the vanilla call with a strike of
   2. times the value of the vanilla call with a strike of
   3. times the value of the vanilla call with a strike of
   4. times the value of the vanilla call with a strike of




3. The supposedly absurd negative risk neutral probabilities can occur in a Cox-Ross-Rubenstein (CRR) binomial tree when:

   1. the volatility of the asset price is considerably less than the absolute value of the cost of carry times the square root of time step;
   2. the volatility of the asset price is considerably higher than the absolute value of the cost of carry times the square root of time step;
   3. the volatility of the asset price is equal to the cost of carry;
   4. Risk neutral probabilities can never become negative in a CRR tree;




4. The sum of a digital call option and a digital put option (with the same strike price) is equal to:

   1. One
   2. the discount factor;
   3. the probability of being in the money for a vanilla call
   4. none of the above




5. An asset is said to be in a "degenerate" state when:

   1. the volatility is zero;
   2. the volatility is infinite;
   3. the volatility is negative;
   4. none of the above

 

Answers:

1(a)
2(a)
3(a)
4(b)
5(a)

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