**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**

- Find CRR put price.

In [ ]:

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**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**

- 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**

- Compute the BSM implied volatility.

In [ ]:

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