Question 2 Let us consider the Black-Scholes Model you studied in Chapter 2. (1) Describe the dynamic or evolution of the share price (main hypoth- esis of BS model). (2) In both the BS PDE proof and the Uniqueness proof we use the Ito's Lemma. Describe in your own words why we can use such theorem. (3) Referring to the proof of the BS PDE, you choose a = -os. Can you describe what the quantity as represent? Why such choice of a implies that the portfolio is risk neutral? (4) Let us consider a call option with underlying So = 40, strike K = 42, maturity T = 2 and implied volatility 20%. What is the value of the implied volatility of a European put option with the same underlying, strike price and time to maturity? Why? (5) The price of a call in the BS model is given as follows; = N(d)S-N(d) Ke-r(T-t) di = In ()+(r+ ) (T t) OVT-t d In()+(- ) ( t) = OVT-t 0 Describe the effect of very high volatility (ie. compute the limit as 00) on the price of the call above. (Hint: Firstly consider what happens to d, and d2). [30] Question 2 Let us consider the Black-Scholes Model you studied in Chapter 2. (1) Describe the dynamic or evolution of the share price (main hypoth- esis of BS model). (2) In both the BS PDE proof and the Uniqueness proof we use the Ito's Lemma. Describe in your own words why we can use such theorem. (3) Referring to the proof of the BS PDE, you choose a = -os. Can you describe what the quantity as represent? Why such choice of a implies that the portfolio is risk neutral? (4) Let us consider a call option with underlying So = 40, strike K = 42, maturity T = 2 and implied volatility 20%. What is the value of the implied volatility of a European put option with the same underlying, strike price and time to maturity? Why? (5) The price of a call in the BS model is given as follows; = N(d)S-N(d) Ke-r(T-t) di = In ()+(r+ ) (T t) OVT-t d In()+(- ) ( t) = OVT-t 0 Describe the effect of very high volatility (ie. compute the limit as 00) on the price of the call above. (Hint: Firstly consider what happens to d, and d2). [30]