Derivatives in Plain Words by Frederic Lau, with a ... - HKU Libraries

Again we use our method of having two strategies which should arrive at thesame result (i.e. a no-arbitrage method). If we assume the forward rate tobe r, starting with $1 today, at the end of 9 months we would either get(I + 5.5% x 9 /n) [A straightforward 9-month fixed rate deposit]or(I + 5%x 6 /i 2 )x(l + r%x 3 /n)[6-month fixed rate deposit, rollover for another 3 months]giving r = 6.34%. This is the interest rate for the period between 24/7/97and 24/10/97 as of today, and is equivalent to a quoted futures price of(100 - 6.34) = 93.66.If today's date becomes 24/4/97. At this day, the 3-month rate has become6%, whereas the 6-month rate is 6.5%. The forward rate for the periodbetween 24/7/97 and 24/10/97 is then calculated by:(I + 6.5% x 6 /i2)(I + r% x 3 / l2 ) = - - '(I + 6% x 3 /i 2 )which gives r = 6.90% (or a futures price of 93.10).What is the implication on the profit-and-loss of the trade? If this is markedto market, it implies that there is a 56 basis point loss (93.66 - 93.10) if theposition in the futures contract is to be closed out immediately. If this isa US dollar futures contract and the notional amount is US$ 1 ,000,000, theloss converts to $1,000,000 x 0.0056 x 3 /i2= $1,400.The above examples give an illustration of a method of calculating interestrate forwards. Alternatively, we can express the calculation in a more generalway. Recalling the definition of the discounting factor (DF, the amount todaywhich represents a future value of $1 using today's interest rate), we see thatin the first example the discounting factors for 6-month and 9-month are= 0.9756, ., DF9-mth - = --- = 0.9604(!+5%x 6 /i2) (l+5.5%x 9 /. 2 )Forwards and Futures