Question

In this task consider a put option with: S0 = 100 E = 100 Rf = 4% Sigma = 15% T = 5 m = 200 Use the binomial option pricing model to check the sensitivity of the option price to changes (each change separately from the other changes) in the parameters. What if:

1. Rf ranges from 0.01 to 0.10 in steps of 0.001
2. Sigma ranges from 0.01 to 0.5 in steps of 0.1 3. m ranges from 5 to 1000 in steps of 10
3. S0 ranges from 50 to 150 in steps of 1
For each change, graph the option price (y-axis) against the parameter you are changing (x-axis). What do we learn about option prices from this analysis? Explain in detail with the underlying economic intuition for these effects!

Answer 1

The student wants to understand how the price of a put option is influenced by changes in various underlying parameters according to the binomial option pricing model. Through constructing graphs, one can observe the effects of changing risk-free rates, volatility, number of steps in the pricing model, and initial stock prices on the option value.

Step-by-step explanation:

The student is asking about the sensitivity of a put option price to changes in various parameters using the binomial option pricing model. This involves performing a series of computations to determine how option prices are affected by changes in the risk-free interest rate (Rf), stock price volatility (Sigma), the number of steps in the binomial model (m), and the initial stock price (S0). We can learn the responsiveness of the put option's price to each parameter by observing the resultant graphs. For example, an increase in Rf generally decreases the value of a put option, as the cost of carrying cash becomes higher. A higher Sigma usually leads to a higher option price due to increased uncertainty. The number of steps m affects the accuracy of the model, with more steps leading to a more precise outcome. Lastly, changes in the initial stock price S0 have a direct impact on the intrinsic value of the put option.