SharedMidterm_V01-Mock.ipynbOpen in CoCalc
MockTest

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 α^\hat \alpha for the approximation of a deterministic number α\alpha. Recall that Bias is given by Bias=E[α^]α.Bias = \mathbb E[\hat \alpha] - \alpha. and the mean square error is given by MSE(α^)=E[(α^α)2].MSE(\hat \alpha) = \mathbb E[ (\hat \alpha - \alpha)^2 ].

Questions

  1. Prove that MSE(α^)=Bias2+Var(α^).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.