1. (Derivative Pricing with one-period Binomial tree model) Given a one-period Binomial tree model: The continuously compounded) risk-free interest) rate is r = 0. The underlying stock price is So = 100$ today, its up-factor and down-factor after T = 1 year are u = 2 and d = 0.5, and the probabilities of the stock price's up and down movements are pu = 0.9 and pa=0.1. (1) Check the no-arbitrage principle is satisfied. (2) A call spread pays off the difference of two call options at maturity T, that is (St - K1)+ - (ST - K2)+ with Ki 0 by discussing two cases K > ST and K 5 Sr. Then show the payoff of the above butterfly is equal to (K3 - Sr)+ 2(K- ST)+ + (K1 - ST) (5) A straddle pays off the sum of a call option and a put option with the same strike at maturity T, that is (ST-K)+ +(K - ST)+. Price a straddle with K = 100. = 1. (Derivative Pricing with one-period Binomial tree model) Given a one-period Binomial tree model: The continuously compounded) risk-free interest) rate is r = 0. The underlying stock price is So = 100$ today, its up-factor and down-factor after T = 1 year are u = 2 and d = 0.5, and the probabilities of the stock price's up and down movements are pu = 0.9 and pa=0.1. (1) Check the no-arbitrage principle is satisfied. (2) A call spread pays off the difference of two call options at maturity T, that is (St - K1)+ - (ST - K2)+ with Ki 0 by discussing two cases K > ST and K 5 Sr. Then show the payoff of the above butterfly is equal to (K3 - Sr)+ 2(K- ST)+ + (K1 - ST) (5) A straddle pays off the sum of a call option and a put option with the same strike at maturity T, that is (ST-K)+ +(K - ST)+. Price a straddle with K = 100. =