Midterm Mock Test

• Name and Student ID:

• Two-hour exam

• Write all your answers on the exam paper. Your answer must be justified clearly

• If you have used python code, you shall convert it into PDF and send it to [email protected]

• It is open book. However, any kind of communication during the exam period is not allowed

Problem 1

Consider CRR option with the following parameters:

• Model: 2-period CRR for total length 2 year

• Stock initial price: 50

• Volatility: 20 %

• Rate: 5 %

• Put option price: 50

• Put maturity: 2 year

Questions

1. Find CRR put price.

Problem 2

Suppose a Monte-Carlo method generates a random variable $\hat \alpha$ for the approximation of a deterministic number $\alpha$. Recall that Bias is given by $$Bias = \mathbb E[\hat \alpha] - \alpha.$$ and the mean square error is given by $$MSE(\hat \alpha) = \mathbb E[ (\hat \alpha - \alpha)^2 ].$$

Questions

1. Prove that $$MSE(\hat \alpha) = |Bias|^2 + Var (\hat \alpha).$$

Problem 3

Consider the following data sets:

Today: Oct 08, 2018

BAC Spot price: 30.27

European Call Maturity: Jun 21, 2019

European Call Strike: 30.0

rate: 0.0264

Market call price: 2.70

Questions

1. Compute the BSM implied volatility.