1. Suppose the current stock price is $110, the exercise price is $105, the annually compounded interest rate is 4%, and the quoted call price
1. Suppose the current stock price is $110, the exercise price is $105, the annually compounded interest rate is 4%, and the quoted call price is $6.50 for a half year option. Identify the appropriate arbitrage opportunity and show the appropriate arbitrage strategy (MAKE A TABLE). Round to 4 decimals. I want an answer to the question number.1
I have posted a sample problem below the way the professor wants his answers to be which is very important.
EXAMPLE PROBLEM
Suppose the current stock price is $100, the exercise price is $100, the annually compounded interest rate is 5%, the stock pays a $1 dividend in the next instant, and the quoted call price is $3.50 for a one year option. Identify the appropriate arbitrage opportunity and show the appropriate arbitrage strategy. - Check violation of lower bound sine dividends exist lower Bound Celso, t, x) = Max [o, so ro-X (1+r)-7] ? Man [, 100-1 -100(16.0s)") -3.76 3,76 3.50 quoted call This arbitrage opportunity (buy call) POC t-T Arbitrage Stratagy tao SEX Sp>y St-X Long call - 3.50 Soad short stock +(100-1) -St Lead with face value of x - 10011.05) =-95.24 +X +X Net +,26 x-st 0 1 positive * lieed positive of tudity with No duensible risk in the future, Notice if St=120 t=T Long call +(120-100) 11 +2o short stock - 120 :-120 Lend with face value of X +100 tlou a exactly enough to fund purchase of stack Need of from short sale Celso,T,x) = MAX [o, so-X (Hot -X (] Note the following standard symbols o So = current stock price (time 0 = today) o T = time to expiration* or=risk free rate** o St = stock price at option's expiration o C(So,T,X) = price of a call option o P(So,T,X) = price of a put option If options can be either American or European options o Ca(So,T,X) = price of a call option => American call o Ce(S0,T,X) = price of a put option => European call Suppose the current stock price is $100, the exercise price is $100, the annually compounded interest rate is 5%, the stock pays a $1 dividend in the next instant, and the quoted call price is $3.50 for a one year option. Identify the appropriate arbitrage opportunity and show the appropriate arbitrage strategy. - Check violation of lower bound sine dividends exist lower Bound Celso, t, x) = Max [o, so ro-X (1+r)-7] ? Man [, 100-1 -100(16.0s)") -3.76 3,76 3.50 quoted call This arbitrage opportunity (buy call) POC t-T Arbitrage Stratagy tao SEX Sp>y St-X Long call - 3.50 Soad short stock +(100-1) -St Lead with face value of x - 10011.05) =-95.24 +X +X Net +,26 x-st 0 1 positive * lieed positive of tudity with No duensible risk in the future, Notice if St=120 t=T Long call +(120-100) 11 +2o short stock - 120 :-120 Lend with face value of X +100 tlou a exactly enough to fund purchase of stack Need of from short sale Celso,T,x) = MAX [o, so-X (Hot -X (] Note the following standard symbols o So = current stock price (time 0 = today) o T = time to expiration* or=risk free rate** o St = stock price at option's expiration o C(So,T,X) = price of a call option o P(So,T,X) = price of a put option If options can be either American or European options o Ca(So,T,X) = price of a call option => American call o Ce(S0,T,X) = price of a put option => European call
