Variable Annuity Contract Company Z issues a contract where the investor invests $100. Funds are invested in a basket of assets and 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 make up 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 Characteristics

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 = [0.03 0.1] + 0.01 o Interest rates and stock returns are uncorrelated

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 breakeven charge for this product?

c) What is the VaR at the 10 percent lower level for company Z?

d) What is the breakeven rate if interest rates are 1% flat?

e) What is the breakeven rate if the initial basket of Stock/Cash is 60%/40%?