here is a homework of course quantitative finance. need help!
of these bonds would you recommend that GoldBank boys or sells in order to protect against an immediate 1% rise in rates (i.e., to protect against an instantaneous parallel shift of the initial yield curve]. ((1) Dene the vega of the swaption to be the change in the swaption value if the volatility increases from [1.6% to [1.7%. What is the vega of the reoeiver swaption? (e) Briey explain why the delta in part (c) is positive or negative. Briey explain Why the vega in part ((1) is positive or negative. 1. {Municipal hot-rowing} Here is an excerpt from "Bridging the decit gsp.'I an article which appeared in RISE magaaine: [5.5. municipalities are writing large vulumes of swaptions to help plug ballooning budget decits. Marc Fireman. treasurer of the New Jersey-based Delaware River Port Authority [DRPA]. could make a killing out ofderivatives this year. The authority. a regional transportation and economic development agency. is considering writing $50 million notional in swaptions at some point in the rst quarter. Ft'raasen1 like many of his counterparts at other US. municipal bodies. is eyeing the big upfront payments investment banks are willing to make for the optionality embedded in the debt that this relatively small local government body which mainly operates bridges and commuter trains - issues. For example. say a LLB. local authority is paying a listed 5% on debt it has already issued. but has the right to call the securities in three year's time at par. The going rate on current L'.S. tart exempt debt is about 4.5%. a dealer. Will. therefore. be willing to pay to have the option to receive the ahevemarltnt ti'iii rate three years from new and in return pay the local authority a oating rate. If market rates are still less than hit three years ionn ooa'. the dealer will escape the option and start to receive a premium oaahilew from the authority. The local authority would then typically issue variable rate refunding bonds. and so pay a heating rate to investors while receiving a oating rate from the dealer. It is. hoe-lever. leit with the ahevemarltet lined payment to the swapticns dealer. "The issuer is stuclt paying his old rate. but in exchange icr that. he get an option premium payment. so he tool: he payment upfront." says .l'eil' Fearsell. Philadelphia- based manager of the straps and derivatives practice at Public Financial Management. an advisory company. Eil' course. if interest rates more above the cpticn's strike price. the local authority has no refunding problem and simply pcclnets the option premiums. In theory it 1rrould usually be easier for the issuer to strip all the call option embedded in the bond and sell that as a separate instrument. But that is not possible under current L13. tart laws on tart-exempt securities. This problem asks you to analyse this transaction using a Hon-Lee interest rate lattice with armual time increments and an initial yield curve which is given in the le hue.sls. All rates in. the spreadsheet are continuously compounded rates. DHPA has it'll] million face amount outstanding of 125% coupon debt. The bonds have lil years remaining until their maturity and are callable at par three years from now. The bond coupons are payed annually [i.e.. a $125 coupon payment is made every year for each $10!] face amount}. Ignore any tart considerations in this problem. GoldBanlt has offered to buy a 3-year European swaption from DRPA. If GoldBanlt exercises the sarapticn. they will receive ?.25% xed and pay oating in a swap. The 125% xed rate is a simply compounded rate. to match the debt payments of the DRPA bond. If the receiver swaption is exercised by GcidElanlr in three years. the swap would have a 'i-year maturity at that time. The underlying notional of the swap is ll million. {a} 1|i.l'i"hat is the Eair dollar price today ofthe receiver swaption assuming a notional oflil million? [bl As an advisor to DRPA. briey explain the advantages and disadvantages of selling this swaption to GoldBanlt. Be as specic and quantitative as possible. to} Suppose that [EPA and GoldBanlt execute the swaption transaction today. GoldElanlr plans to hedge the swaption by buying or selling ve-year zero coupon bonds. What Eace amount
