Part e1. In 1973, Fisher Black and Myron Scholes developed the Black-Scholdes option pricing model (OPM). What assumptions underlie the OPM?
Answer. There are several assumptions underlying the OPM. First, the stock underlying the call option provides no dividends or other distributions during the life of the option. Second, there are no transaction costs for buying or selling either the stock or the option. Third, the short-term, risk-free interest rate is known and is constant during the life of the option. Fourth, any purchaser of a security may borrow any fraction of the purchase prices at the short-term, risk-free interest rate. Fifth, short selling is permitted, and the short seller will receive immediately the full cash proceeds of today’s …show more content…
What is put-call parity? According to Brigham and Ehrhardt (2014), if two portfolios have identical payoffs, then their values must be identical. In the case of a put option and a call option with the same strike price and expiration date, suppose one portfolio contains the put option plus one share of stock, and the other portfolio contains the call option plus some cash, then at the expiration date, the strike price of the stock will equal the value of the cash. In other words, the put-call parity relationship states that Put option + Stock = Call option + PV of exercise price.
Plaehn (2017) added although puts and calls at the same strike price should offer the same opportunity for a return which is based on price changes of the underlying stock, real world market conditions can cause the option prices away from parity. First, put and call parity only works for European style options which can only be exercised on the expiration date. For American style options, the chance of early expiration distorts the calculations. Second, other factors which affect options prices include bid-ask spreads, manipulations from market makers, type of market (e.g. bull or bear markets) and trader sentiment. A trader can take advantage of the slippage in parity by comparing equivalent strategies and select the one with the slightly higher potential return (Plaehn,
Answer. There are several assumptions underlying the OPM. First, the stock underlying the call option provides no dividends or other distributions during the life of the option. Second, there are no transaction costs for buying or selling either the stock or the option. Third, the short-term, risk-free interest rate is known and is constant during the life of the option. Fourth, any purchaser of a security may borrow any fraction of the purchase prices at the short-term, risk-free interest rate. Fifth, short selling is permitted, and the short seller will receive immediately the full cash proceeds of today’s …show more content…
What is put-call parity? According to Brigham and Ehrhardt (2014), if two portfolios have identical payoffs, then their values must be identical. In the case of a put option and a call option with the same strike price and expiration date, suppose one portfolio contains the put option plus one share of stock, and the other portfolio contains the call option plus some cash, then at the expiration date, the strike price of the stock will equal the value of the cash. In other words, the put-call parity relationship states that Put option + Stock = Call option + PV of exercise price.
Plaehn (2017) added although puts and calls at the same strike price should offer the same opportunity for a return which is based on price changes of the underlying stock, real world market conditions can cause the option prices away from parity. First, put and call parity only works for European style options which can only be exercised on the expiration date. For American style options, the chance of early expiration distorts the calculations. Second, other factors which affect options prices include bid-ask spreads, manipulations from market makers, type of market (e.g. bull or bear markets) and trader sentiment. A trader can take advantage of the slippage in parity by comparing equivalent strategies and select the one with the slightly higher potential return (Plaehn,