True or False?

a. Add a short position of zero-coupon bond will shift down the prot diagram of an existing option position.

b. An option position with a prot diagram always below zero indicates an arbitrage opportunity (ignoring transaction costs and shorting constraint).

c. Both the long position and the short position of one share of European call option have the same break-even price of the underlying asset.

d. The put-call parity applies to both American and European options.

4 e. One can create a synthetic short position of stock by holding a long position of call option, a long position of put option, and a short position of zero-coupon bond (both the call and the put are European options with the same stike price, the same maturity, and the same underlying asset, which is the stock).

f. The Black-Scholes price is the limiting case of the Binomial option price with an innite number of time steps.

g. In order to price an option, one needs both the expected return and the volatility of the underlying asset.

h. The Black-Scholes formula assumes no transaction costs when trading the underlying asset.

i. The put-call parity does not hold for the Black-Shooles formula of call option price and put option price.

j. The delta of an option is also called the hedging ratio.