#4 Standard Forward Rate Agreements - Incorporating Bid-Offer Spreads At the current date to, assume the...

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#4 Standard Forward Rate Agreements - Incorporating Bid-Offer Spreads At the current date to, assume the existence of a set of term structures of simple bid, mid and offer spot interest rates, denoted by {R(to, 8), R(to, 8), Ro(to,s)},to respectively, with associated capitalisation and discount factors (CB(to, 8), C(to, s), Co(to,s)}, and {ZB(to, 8). Z(to, 8). Zo(to, 8)}>>t, respectively. (i) For a generic standard FRA, assuming the initiation date is to, settlement date is t, and expiry date is te, show that the theoretical fair FRA bid rate is [f(to:ts.te) + RB(t,,te) - R(t,,te)], where fa(toits.te)= (Zo(to.t.) = (ZB (to, te)-1). and the theoretical fair FRA offer rate is [fo(to;t,,te) + Ro(t,,te) R(t,,te)], where fo (to; ts,te) == (Zo(fo,fe) 1 (ZB(to.t.) .-1). from the perspective of a market-maker, where = (te - ts)/365 and R(s, t) := [RB(s, t) + Ro(s, t)]/2 is the mid reference rate used for settlement for all to are actually forward bid and offer rates, respectively. 8 #4 Standard Forward Rate Agreements - Incorporating Bid-Offer Spreads At the current date to, assume the existence of a set of term structures of simple bid, mid and offer spot interest rates, denoted by {R(to, 8), R(to, 8), Ro(to,s)},to respectively, with associated capitalisation and discount factors (CB(to, 8), C(to, s), Co(to,s)}, and {ZB(to, 8). Z(to, 8). Zo(to, 8)}>>t, respectively. (i) For a generic standard FRA, assuming the initiation date is to, settlement date is t, and expiry date is te, show that the theoretical fair FRA bid rate is [f(to:ts.te) + RB(t,,te) - R(t,,te)], where fa(toits.te)= (Zo(to.t.) = (ZB (to, te)-1). and the theoretical fair FRA offer rate is [fo(to;t,,te) + Ro(t,,te) R(t,,te)], where fo (to; ts,te) == (Zo(fo,fe) 1 (ZB(to.t.) .-1). from the perspective of a market-maker, where = (te - ts)/365 and R(s, t) := [RB(s, t) + Ro(s, t)]/2 is the mid reference rate used for settlement for all to are actually forward bid and offer rates, respectively. 8