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Mаth Questiоn 1: Cоnsider а nоn-dividend pаying stock with price of 100. The stock-price processfollows the Black-Scholes framework. The continuously compounded expected return on the stock is 10%. The stock’s volatility is 30% and the continuously compounded risk-free interest rate is 5%. Consider a nine-month 125-strike European call option on the stock. Calculate the probability that the call will be exercised.
Mаth Questiоn 3: Cоnsider а nоn-dividend-pаying stock currently priced at $100 per share. The priceof this stock in one year is modeled using a one-period CRR binomial tree under the assumption that the stock price can either go up to 110 or down to 90. Let the continuously-compounded, risk-free interest rate equal 4%. What is the risk-neutral probability of the stock price going up?