写作ECON41415/WE01编程、辅导Python编程设计

” 写作ECON41415/WE01编程、辅导Python编程设计EXAMINATION PAPERExamination Session:ECON41415/WE01Title:Derivative MarketsTime Allowed: 2 hoursAdditional Material provided: NoneMaterials Permitted: NoneCalculators Permitted: Yes Models Permitted:Only the following list Of calculators is permitted inthis examination: Casio FX83; Casio FX85; TexasTI-30XS; Sharp EL-531. Calculators with additionaltext after model designations are acceptable (e.g.Casio FX85GT). Other Models of calculator will notbe considered on the day of the examination. Ifyour calculator is not permitted, it will beconfiscated.Visiting Students may use dictionaries: NoInstructions to Candidates: Answer one question from Section A which accounts for 50% ofthe total marks.Answer one question from Section B which accounts for 50% ofthe total marks.Revision:Page 2 of 5 ECON41415/WE01Section AQuestion 1The following table gives the current prices of bonds. Half the stated coupon is assumed to be paidevery six months.Bond Bond principal 写作ECON41415/WE01作业、辅导Python编程Time to maturity(years)Annual coupon($)Bond price($)Treasury bond A 100 0.5 2.0 100Treasury bond B 100 1.0 4.0 98Treasury bond C 100 1.5 4.0 98Corporate bond D 100 1.0 6.0 98a) Define the term zero rate and explain how zero rates are determined using the bootstrap method.Calculate the zero rates with continuous compounding for the maturities of 0.5, 1.0 and 1.5 years.Present the theories of the term structure of interest rates. Discuss which theory can best explain theterm structure Iimplied by the current example.(30 marks)b) Explain the concept forward rate and calculate the forward rate for the period between 0.5 years and1.5 years. Discuss also the term par yield and explain how the par yield is calculated. Determine thepar yield for the maturity of 1.5 years. Report the par yield with continuous compounding.(30 marks)c) Explain the term bond yield (YTM). Determine the YTM of corporate bond D. Explain the concept ofzero-volatility spread (Z-spread). Check which of the following rates better approximates the Z-spreadof corporate bond D: 1.18% or 1.98%. Explain the term Macaulay duration and determine theMacaulay duration of the bond. Explain how duration is used in portfolio risk management.(40 marks)Page 3 of 5 ECON41415/WE01Question 2Company Alpha, a British manufacturer, is required to borrow US dollars at a fixed rate of interest. CompanyBeta, a US multinational, is required to borrow sterling at a fixed rate of interest. The two companies havebeen offered the following borrowing rates per annum with semi-annual compounding on 100 million and$122 million for two years. Interest payments are to be made every six months.GBP USDCompany Alpha 3.0% 5.6%Company Beta 2.0% 3.0%a) Explain the term comparative advantage and discuss why currency swap can be motivated bycomparative advantage. Assume that a swap is arranged in which a financial institution acts as anintermediary between The two companies. Design a currency swap that is equally beneficial for thetwo companies assuming that the financial institution earns 20 basis points per annum and bears theentire foreign exchange risk. Show your calculations and use a diagram to explain how the swap isarranged.(30 marks)b) Assume that the swap has a remaining life of 15 months to maturity and the term structure of interestis flat in both currencies. The USD interest rate is 3% per annum and the GBP interest rate is 2% perannum, both reported with continuous compounding. The spot exchange rate GBP/USD is 1.10.Determine the value of the currency swap for Company Alpha.(30 marks)c) Discuss the risks for the counterparties in a currency swap. Discuss the scenarios in which these risksarise and whether these risks can be hedged. Suppose that six months before the final exchange ofpayments in the Swap company Alpha declares bankruptcy and defaults on its current and futureswap payments. Calculate the losses that arise as a result of the default and explain which partybears these losses. Use the same interest rates and exchange rate in your calculations as in Part b).(40 marks)Page 4 of 5 ECON41415/WE01Section BQuestion 1a) Critically discuss the assumptions about asset price dynamics in the standard option pricing models.Explain the factors that these models consider and the effect of these factors on the prices ofEuropean call and put options.(30 marks)b) Assume that the current price of a non-dividend paying stock is 0 =40. In the next six months, thestock price can either increase by 20% or decrease by 10%. Assume that the risk-free interest rate isr=0% per annum. Consider a 6-month European call option with a strike price of K=40. Explain theno-arbitrage argument for pricing options. Determine the option price using the no-arbitrageapproach. Explain all your calculation steps.(30 marks)c) Assume that the current exchange rate GBP/USD is 0=1.23 and in the next six months it can eithermove up to 1.30 or down to 1.10. The risk-free interest rate in GBP is 1.5% and in USD is 2.5% perannum (reported with continuous compounding). Determine the value of a six-month Europeanexchange rate put option (i.e. to sell GBP) with a strike price of K=1.25 and a contract size of 10,000GBP.(40 marks)Page 5 of 5 ECON41415/WE01Question 2A stock price follows A geometric Brownian motion with expected return and a volatility : = + Its lemma states that if is a function of and ,The Black-Scholes formula for the price of a European call option is given by Two derivatives On the stock are proposed with values (,) = and (,) = . Use Itslemma to examine whether these new derivatives also follow a geometric Brownian motion.(30 marks)b) Critically discuss the assumptions on the return dynamics of the underlying asset in the Black-Scholesmodel. Explain the effect of the model parameters on option prices.(30 marks)c) Consider a stock with a current price of $20 and a volatility of 20% per annum. Assume that the currentrisk-free interest rate is 5% per annum reported with continuous compounding. Determine the priceof a European put Option on the stock with a strike price of $15 and an expiration date in six months.Express your answers in terms of the cumulative normal distribution ().(40 marks)END OF EXAMINATION如有需要，请加QQ：99515681 或邮箱：99515681@qq.com

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