# Delta Of A Forward Rate Agreement

Generally speaking, the above analysis reminds us that we need to consider all the factors that move with the share price when determining the right delta for a futures contract. Delta is defined as the ratio between the change in the price of a derivative instrument and the change in the price of the underlying. It is therefore quite natural that any factor with a sensitivity to value relative to the underlying stock should have an impact on the delta of the futures contract and differ from another. In addition to dividends, borrowing costs related to hedging and balance sheet utilization costs are examples of such factors. The right hedge for futures doesn`t always have a delta equal to one. Dividends, borrowing costs and balance sheet utilization costs are examples that could make the delta different when it comes to futures. In determining the appropriate delta of a futures contract, derivatives professionals must consider all factors that are sensitive to the price of the underlying asset. It is important to note that \$F (t, T)\$ is not an asset: after all, the discount value of \$F (t, T) \$n clearly not a martingal below the risk neutral ratio. It is more natural to take the delta of the futures contract, which is an asset.

The same applies when the ABC share pays a fixed dividend, for example USD 1 per year. The selling price at the front of one year, in turn using the cash and carry formula, will be 99 USD. To put delta coverage, borrow \$100 today and buy an ABC stock. During the year, you will receive dividends of USD1. After a year, deliver the stock and receive \$99. With \$100 in your hands, you`ll pay off your loan in full (\$99 on the futures contract and \$1 in dividends). The Delta One strategy is still working. The FRA sets the rates to be used at the same time as the date of termination and the nominal value. FRA are settled in cash on the basis of the net difference between the interest rate of the contract and the market variable rate called the reference rate. The nominal amount is not exchanged, but a cash amount based on price differences and the nominal value of the order. So, what is the Delta for the duration of the dividend? Unsurprisingly, it`s .01: for contracts at the front, I @Matt agree that its delta is only one. But is this still true? Below is a brief example showing that a futures contract does not necessarily have a delta equal to one.

To simplify the calculations, suppose the interest rates are 0 (r = 0%). Company A enters into a FRA with Company B in which Company A obtains a fixed interest rate of 5% on a face value of \$1 million in one year. In return, Company B receives the one-year LIBOR rate set over three years on the nominal amount. .