Valuing and Transferring an Existing Forward Contract

# Some questions on (re-)pricing a forward


# Some questions on (re-)pricing a forward












A few questions and my answers, to be sure I understand everything

Question 1

Suppose A and B agree on a forward contract: maturity

- $T = 1Y$

- spot at $t=0$: $S_0=100$

- forward price $K = 120$.

Suppose B wants to sell this contract to C at $t = 6M$ (so that the contract will be between A and C). Suppose that $S_{6M}=135$, then C will buy the contract at 135-120=15 ?(so C buys the mark-to-market forward price)

Question 2

The value of a forward contract at $t$ = 0 equals

$$V_{0}=S_{0}-Kexp(-rT)$$

with $K=S_{0}exp(rT)$.

At $t = 6M$, the value is

$$V_t=S_t-Kexp(-r(T-t))=S_t-S_{0}exp(rT)exp(-r(T-t))=S_t-S_0exp(rt).$$

So again C will buy the contract at this price (?)

## Answer by Gordon (score 4)

https://quant.stackexchange.com/a/35551

Assuming zero dividend and a constant interest rate $r$, the 1y forward price is then \begin{align*} 120 = K = S_0 e^r = 100\, e^r. \end{align*} Consequently, $e^r = 1.2$. The fair value of the forward contract, at 6M, is given by \begin{align*} e^{0.5 r} E\left(\frac{S_{1Y}-120}{e^{r}} \mid \mathcal{F}_{6M} \right) &= e^{0.5 r}\left(\frac{S_{6M}}{e^{0.5 r}} -\frac{120}{e^r}\right)\\ &= S_{6M} - 120 e^{-0.5 r}.\tag{1} \end{align*}

Then, for your Question 1, C is willing to buy the forward contract with the price 135-120 = 15, given that the value in $(1)$ is greater than 15.

For your second question, since \begin{align*} S_t - S_0 e^{rt} &= S_{6M} - S_0 e^{0.5r}\\ &= S_{6M} - S_0 e^r e^{-0.5r}\\ &=S_{6M}- 120 e^{-0.5 r}, \end{align*} C is indifferent for buying the forward contract with this price.