关键词 > ISE563
ISE 563 Spring 2024
发布时间：2024-05-09
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
ISE 563 Spring 2024
Due: May 3, 2024
Instructions:
• Answer questions below in a 1– 2-page memo explaining your methodology and findings
• Describe how you gauge the reasonableness of the results
Extended Exercise – Variable Annuity Contract
Company Z issues a contract where the investor invests $100. Funds are invested in abasket of assets with the following guarantee. The investor is guaranteed to withdraw 5% of the base 100 value per year (at the end of the year). Guarantee is independent of the portfolio performance. If the portfolio runs out of money, Company Z must makeup the difference for the remainder of the contract. For this guarantee, the investor pays company Z 2% per year on the outstanding balance each year. Assume the contract runs for 30-years at which point any money remaining is returned to the investor.
Investment Basket Assumptions
a) $90 in Stock 1
o Implied volatility of 20%
o Real World volatility of 15%
o Real World drift of 8%
b) $10 of Cash
o Returns the risk-free rate
Other Assumptions
• Fees are taken out before the withdrawal is made.
• Simulate using annual steps.
Risk-Neutral Risk-Free Rates
• Assume the term structure is flat and parallel shifts are driven by:
o dT = 0.1[0.03 − T]dt + 0.01d
o Interest rates and stock returns are uncorrelated
o Initial interest rate is 5%
Questions
a) Calculate the profit/loss for the insurance company that nets the fees collected against the money paid out if the portfolio runs out of money. Value using 100 simulations or more with annual steps. Do the problem assuming no rebalancing to the initial 90%/10% mix.
b) What is the value if interest rates are 1% flat?
c) What is the breakeven charge for this product?
d) What is the VaR at the 10 percent lower level for company Z?
e) What is the value if the initial basket of Stock/Cash is 60%/40%?
