Q2. Underlying follows lognormal distribution and is current at $100 with annual volatility of 40%. There are three months b/f expiration. Riskfree rate of zero. You construct a PUT front ratio - long one put at 50 delta and short 2 put at 25 delta.

Q2a. What is the strike of the two puts you will be using?

(hint: delta of put option is - F(z-new). First find proper z-new that will give you the correct delta location. Then back out strike price from z-new formula

z-new = z-old - sigma * sqrt(T) = [ ln (X/S0) - (rf+1/2*sigma^2) * T] / [sigma * sqrt(T)]

b. What is the gamma of the put front ratio spread?

c. What is the vega value for the 50 delta put and for the 25 delta put respectively? What is the vega value for the PUT front ratio spread? (note: vega defined as option value change corresponding to 1 percentage point change in annualized volatility)

d. Underlying moved down to $95 in one day. IV did not change. What is PnL due to delta, gamma and theta respectively ?

e. Underlying moved down to $95 in one day. Annualized return standard deviation goes up from 40% to 42% for the former 50 delta put and goes up from 40% to 23% for the former 25 delta put. What is the PnL due to vega effect and what is the total PnL from delta+gamma+theta+vega effects?