# Value at Risk - Ch.11: VAR Mapping

#1

Reading Source: Textbook - Value at Risk

• Mapping for Risk Measurement
• Why Mapping?
• Mapping as a Solution to Data Problems
• The Mapping Process
• General and Specific Risk
• Mapping Fixed-Income Portfolios
• Mapping Approaches
• Stress Test
• Benchmarking a Portfolio
• Mapping Linear Derivatives
• Forward Contracts
• Commodity Forwards
• Forward Rate Agreements
• Interest-Rate Swaps
• Mapping Options
• Conclusions
• Appendix A: Assigning Weights to Vertices

#2

In this chapter, it mentions forward contract value and current forward value. What is the difference between this two items? Any help would be greatly appreciated!

#3

The forward contract value is the amount that the purchaser will pay at the expiry date, for the asset in the contract. The value of the forward contract is the present value of the asset minus the present value of the forward price or: Se^(-yt) - Ke^(-rt).
(y is the asset income flow - like dividends) Typically, there is no up-front cost, so the K is solved for to ensure the initial price is 0. This solved for K is the forward contract value.

As time passes however, the value of the stock will change and the value of the forward contract will not always stay at 0. Therefore, re-evaluating the contractâ€™s value: Se^(-yt) - Ke^(-rt) will give you the current forward value.

#4

As the textbook wrote, we can get Ft = (St*e^-yĎ„) * e^-rĎ„ (11.10) by setting ft=0 and K=Ft.
If so, what does the formula (11.11) mean? I think this equation equals to zero eventually.

Any help will be appreciated!

#5

Formula 11.11 will change over time. Initially, it will equal 0 because the contract has been priced such that there is no initial value to the contract because Ft = K. However, as time passes and market conditions change, Ft will no longer = K. You must re-evaluate the equation for Ft as time passes (Use equation 11.10 replace t with the time to maturity of the contract). Then you can plug this â€śupdatedâ€ť value of Ft into equation 11.11 to determine the current value of the forward contract. This can be positive or negative depending on the market conditions.

Let me ask youâ€¦ If I have a long forward contract and letâ€™s say a month has passed. What would have had to happen to the stock value for the forward contract to have positive value for me now?

#6