Value at Risk - Ch.11: VAR Mapping


#1

A Fellowship Forums Wiki Community Post

Online Link to this Reading: N/A

Topics Covered in this Reading:

  • 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


This is a wiki post, editable by anyone. Feel free to edit and add key points/extra detail above!


#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 contract’s value: Se^(-yt) - Ke^(-rt) will give you the current forward value.


#4


Thanks for the replying,

May I ask further questions?
As the textbook wrote, we can get Ft = (St*e^-yτ) * e^-rτ (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!:sweat_smile::sweat_smile:


#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 “updated” 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 you… If I have a long forward contract and let’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

Thanks for the replying,

I think forward contract value will increase if stock value has risen, but stock value is not subject to the fluctuation of forward contract value.:sweat_smile:


#7

You’re right, the value forward contract will go up if the stock price goes up! This is why you would need to re-evaluate equation 11.11 to determine the value of the contract. `

but stock value is not subject to the fluctuation of forward contract value

I’m not sure I follow you here. The stock price will fluctuate naturally on its own, and the value of the forward contract will be derived from the stock movements.