I had an query regarding forward contract, no arbitrage principle, my Questions are;
If in a question given that, suppose the forward price is actually trading at $510 rather than no-arbitrage price at $507.34, is that we enter in a forward contract at initiation for $510 or $510 is the fair value price at expiry?
If we enter in to contract at $510( short) and at expiry we delivery at $510 & we repay $507.34 at expiry(no arbitrage price) we make profit of $2.66 that’s the arbitrage but what if the fair value at expiry is $508 or $511 do we considered as an arbitrage g/l (diff between fair value of underlying at expiry & delivery price)?
That’s the price of the forward: the price to which you agree at initiation that you will pay (or receive) for the underlying at expiration.
I’m not following the “we repay $507.34” part.
If all we’ve done is enter into a short position, then we deliver the underlying and receive the forward price (to which we agreed at initiation). If we don’t already own the underlying, we’ll have to buy it for whatever the market (spot) price at the expiration of the forward.
I’ll speculate that by “we repay $507.34” you mean that the forward was part of an arbitrage transaction: we borrowed the spot price at the initiation of the forward, bought the underlying, and entered into a short position in the forward. If that’s the case, then at expiration of the forward we’ll deliver the underlying (that we already own), receive the forward price (to which we agreed at initiation), repay the loan plus interest, and have a profit left over. In that case, the market (spot) price at the expiration of the forward is irrelevant, because we already own the underlying, so we don’t have to buy it.
Yes absoutly! we borrow $500 and buy in spot at $500 and enter in to short forward at $510, at expiry we deliver at $510 and repay $507.34 and earn the difference, but i still don’t understand why it is irrelevent if the fair value at expiry isgreater then contract price(forward price), $511 is fair value at expiry and $507.34 is forward price, we are selling at lower price then market it should be loss of $1. One more question i have is we should term the $1 as arbitrage loss or pure forward loss? i am stuck with difference in arbitrage gain/loss and pure forward gain/loss. Thank you…
Yes, when you sell at the guaranteed price of $510 you’ll earn $1 less than if you sold at the market price of $511, but you’ll earn $1 more than if the market price were $509. That loss or gain is a pure forward loss/gain; it’s not arbitrage because it’s not certain (risk-free); you have to wait until expiration to know what that value is.