Question

What is a general formula for a lower bound on the price of a put with strike price K, matruity T, and risk-free rate r? Given an arbitrage argument to prove this lower bound.

Answer 1

The general formula for a lower bound on the price is:

where p is the price of the put

K is the strike price

R is the risk free rate of return

T is the time period

S is the current stock price

Suppose, there is a 1-year American put option with a strike price of $97 and a current price of $90 while the risk free rate of interest is 6%.

In this case, the value of the put option is:

So given a chance to sell today at $90 or a year later at $97, if the price of the put is lower than 1.35, the investor would opt to sell by exercising put option however, if the price is greater than 1.35, the investor would like to sell today.