R question

Here is a question and the answer. Please use R to write the code for the formula to obtain the given answer. Thank you.

. (40 points) Consider the case where an asset price, S(t), with initial price $100 is governed by a geometric Brownian motion: S(t)= 100e-0.0950t+0.5B(0), 0 s t o0 where B(t) is a standard Brownian motion (E[B(t)] 0 and cov(B(t), B(7)) min(t, r)) Here the risk-free interest rate is 3% and the stock volatility is 50%. A discretely monitored Asian arithmetic average call option with strike price $100 monitored quarterly (4 times per year) and expiring in one year has a discounted payoff of discounted payoff max SG/4) 100, 0 e -0.03 j=1 With the same parameters and 10 sample paths, estimate the price of the Asian arithmetic average call option. ANSWER Estimate the price of the Asian arithmetic average call option A standard Brownian is a stochastic process (Wt }t,O+ (that is, a family of random variables Wt, indexed by nonnegative real numbers t, defined on a common probability space (,F,P)) Given the parameters the value of call option will be $ 20.932 The same can be derieved by using the formula:- C SN(d,)-N(d2)Ke-rt d In c-Call premium S-Current stock price t-Time until option exereise K-Option striking price r-Risk-free interest rate N-Cumulative standard nomal distribution e-Exponential tem St. Deviation In-Natural Log . (40 points) Consider the case where an asset price, S(t), with initial price $100 is governed by a geometric Brownian motion: S(t)= 100e-0.0950t+0.5B(0), 0 s t o0 where B(t) is a standard Brownian motion (E[B(t)] 0 and cov(B(t), B(7)) min(t, r)) Here the risk-free interest rate is 3% and the stock volatility is 50%. A discretely monitored Asian arithmetic average call option with strike price $100 monitored quarterly (4 times per year) and expiring in one year has a discounted payoff of discounted payoff max SG/4) 100, 0 e -0.03 j=1 With the same parameters and 10 sample paths, estimate the price of the Asian arithmetic average call option. ANSWER Estimate the price of the Asian arithmetic average call option A standard Brownian is a stochastic process (Wt }t,O+ (that is, a family of random variables Wt, indexed by nonnegative real numbers t, defined on a common probability space (,F,P)) Given the parameters the value of call option will be $ 20.932 The same can be derieved by using the formula:- C SN(d,)-N(d2)Ke-rt d In c-Call premium S-Current stock price t-Time until option exereise K-Option striking price r-Risk-free interest rate N-Cumulative standard nomal distribution e-Exponential tem St. Deviation In-Natural Log