For each question, identify the statement as True/False/Uncertain. You must explain your reason for answering True/False/Uncertain. You may use verbal, diagrammatic and mathematical arguments as appropriate.
3) Money printing is the main driver of inflation in the short term (up to 1 year). 4) Assume that, for some time, inflation had been stable at 3%, while the Central Bank target nominal rate was 5%. Now, inflation has suddenly increased to 3.5%. To cool down the economy, the Central Bank must increase its target nominal rate to 5.5%. 5) An investor is expecting the stock price of a big-tech company to go up. Speculating by using forwards/futures is less expensive to buy than using call options (with the same strike price and time-to-maturity). 6) The early exercise of an American put option becomes more attractive as the risk-free rate falls and the volatility of the underlying asset price increases. 7) [The context] A symmetric butterfly spread has positions in options with 3 different strike prices. It can be created by buying a call option with a relative low strike price K, buying a call option with a relatively high strike price K3, and selling two call options with a strike price K2 = 0.5(K1 + K2). It can also be created by using put options. [The statement] The cost of a butterfly spread created from European puts is smaller than the cost of a butterfly spread created from European calls (with the same strike prices and expiration dates). 8) If W4 follows a Brownian motion, then E[W4] = 3t?. [Hint] You can use Ito's Lemma: df (X4) = (fx(X4)(X, t) + 0.5fxx(X4)o?(X, t))dt + fx(xt)o(Xt, t)dWt, where {Xt, t > 0} is an Ito process with u(Xt,t) as the drift and o(Xt,t) as the volatility. 3) Money printing is the main driver of inflation in the short term (up to 1 year). 4) Assume that, for some time, inflation had been stable at 3%, while the Central Bank target nominal rate was 5%. Now, inflation has suddenly increased to 3.5%. To cool down the economy, the Central Bank must increase its target nominal rate to 5.5%. 5) An investor is expecting the stock price of a big-tech company to go up. Speculating by using forwards/futures is less expensive to buy than using call options (with the same strike price and time-to-maturity). 6) The early exercise of an American put option becomes more attractive as the risk-free rate falls and the volatility of the underlying asset price increases. 7) [The context] A symmetric butterfly spread has positions in options with 3 different strike prices. It can be created by buying a call option with a relative low strike price K, buying a call option with a relatively high strike price K3, and selling two call options with a strike price K2 = 0.5(K1 + K2). It can also be created by using put options. [The statement] The cost of a butterfly spread created from European puts is smaller than the cost of a butterfly spread created from European calls (with the same strike prices and expiration dates). 8) If W4 follows a Brownian motion, then E[W4] = 3t?. [Hint] You can use Ito's Lemma: df (X4) = (fx(X4)(X, t) + 0.5fxx(X4)o?(X, t))dt + fx(xt)o(Xt, t)dWt, where {Xt, t > 0} is an Ito process with u(Xt,t) as the drift and o(Xt,t) as the volatility
