Zero coupon bond barrier option

The coupon bond barrier option reduces to the zero coupon case when only one coupon, say the final coupon, is nonzero; hence cN = 1 and ci = 0, i = N. For the barrier functions, the coefficients have the following limits dN = 1 and di = o, i = N and yield fid ^ fi ; v2 'y ' diGiJdJ Gnn = G

The martingale condition yields f = G/2 and hence

V* — [J(e—(g—f) — 1) + F — K ]+; J = e—f = F

Collecting the results above yields, from Eq. (17.53), the following zero coupon limit of the coupon bond barrier option

Cb(0 u, T, K) — B(t0, t*) f e—inQ(F + Q — K) Z

JQ,n

= e—2G dgQ[g, f; G; a, b]eG(g—f)( 1 + in[Je—(g—f) — 1]

The results given above yield that

This is the expected approximation of the exactresult, which is given in Eq. (17.29).

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