2. The current stock price is $80 and the stock pays no dividend. Each month, the...

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2. The current stock price is $80 and the stock pays no dividend. Each month, the stock price is either going up by 3% or going down by 1%. The current interest rate is an APR of 12% with monthly compounding. Consider a 3-month time interval (i.e. we are interested in payoffs occurring three months from now) and use the Binomial Lattice model with 3 timesteps (that is, each month is a period). Find the no-arbitrage price of the following options. (a) A European put option with strike price $80. Answer. (b) A European option that you can choose exercise either as regular put or call option with strike price $80 at the end of the 3-month period. Answer. (c) A European digital call option with strike price $80. The payoff of this option is zero unless the corresponding European call option has a positive payoff in which case the payoff is $1. The payoff Cd at maturity is thus: Answer. 0 if ST K cd = if ST > K (d) A European digital put option with strike price $80. The payoff of this option is zero unless the corresponding European put option has a positive payoff in which case the payoff is $1. The payoff Po at maturity is thus: Answer. 0 if ST > K Po = 1 if ST < K 2. The current stock price is $80 and the stock pays no dividend. Each month, the stock price is either going up by 3% or going down by 1%. The current interest rate is an APR of 12% with monthly compounding. Consider a 3-month time interval (i.e. we are interested in payoffs occurring three months from now) and use the Binomial Lattice model with 3 timesteps (that is, each month is a period). Find the no-arbitrage price of the following options. (a) A European put option with strike price $80. Answer. (b) A European option that you can choose exercise either as regular put or call option with strike price $80 at the end of the 3-month period. Answer. (c) A European digital call option with strike price $80. The payoff of this option is zero unless the corresponding European call option has a positive payoff in which case the payoff is $1. The payoff Cd at maturity is thus: Answer. 0 if ST K cd = if ST > K (d) A European digital put option with strike price $80. The payoff of this option is zero unless the corresponding European put option has a positive payoff in which case the payoff is $1. The payoff Po at maturity is thus: Answer. 0 if ST > K Po = 1 if ST < K