Let's have a look into a worked numerical example.

Say we have a view that rates will fall, that is futures, prices will rise and we wish to express that view using a stir option.

The December future is trading at 95 25, which if we ignore the small effect of convexity implies a rate of 4.75%.

We've got an at the money ninety five twenty five call option, which is quoted at a price of point 16 points.

The option contract size is two and a half thousand dollars per point, the same as the futures contract, which corresponds to the usual $25 per basis point.

Now, let's assume you buy a thousand calls at point 16 and we'll calculate the answers to the questions on the screen.

The cash premium is given by multiplying the price of point 16 by the contract size of two and a half thousand dollars to get $400 per option contract.

We then multiply that by the position size of 1000 contracts to get a total premium of $400,000.

The break even of the position can be easily approximated using the option price option for the call option to break even The future's price needs to move up by point 16 points to a price of 95 41.

That is to say that the implied rate would need to fall by 16 basis points to 4.59%.

This, however, is only the exact answer.

If we ignore discounting effects in practice, the exact breakeven answer would depend on premium financing costs and margin interest rates.

However, 95 41 works as a good approximation.

There are two ways to compute the profit and loss on the trade.

Firstly, we can compare the payoff of the option to the premium paid.

If the futures price is at 95 52 on expiry, the option payoff is point 27 points, which is 95 52 minus the strike of 95.

25. Multiply this payoff by the two and half thousand dollars contract size and the position of 1000 contracts, and we have a cash payoff of $675,000.

If we subtract the $400,000 premium you paid, then that gives a net profit of $275,000.

The second way of calculating your p and l is to look at the difference between the final futures price and the option break even.

We calculated before, remember, the break even is the point where your net p and l would be zero.

The difference between the final Price of 95 52 and the break even of 95, 41 is point 11 points.

If we multiply this difference by two and half thousand dollars per contract and the position of 1000 contracts, we get a net profit of $275,000.

The same as before.