这个作业是计算商品利率、掉期价值等金融属性
FNCE 403 v4: Assignment 3
问题1.普通香草利率掉期（20分）
儿童玩具制造商Incredible Inc.进行了为期两年的普通利率互换，在该互换中，公司将获得固定利率并以LIBOR的浮动利率支付费用。此次掉期的名义金额为7500万美元。掉期付款将每180天扣除一次，LIBOR需要假设一年为360天。互换开始日的LIBOR期限结构如下：
天率（％）
180 3.50
360 3.55
540 3.60
720 3.70
一个。在掉期起始日确定的固定利率是多少？ （6分）
b。计算起始日期的掉期值。 （1分）
C。掉期的第一笔净付款是多少？谁付款，不可思议的公司还是掉期交易商？ （1分）
d。假设现在交换期限为120天。 LIBOR的新期限结构如下：
天率（％）
60 3.60
240 3.70
420 3.80
600 3.90
计算第120天的掉期价值。（6分）
e。假设现在交换期限已经360天了。 LIBOR的新期限结构如下：
天率（％）
180 3.85
360 3.90
540 3.95
720 4.00
在第540天计算掉期的净付款，在第360天计算掉期的价值。（6分）
问题2.货币掉期（20分）
一家加拿大公司（ACC）刚刚与Big Dealer Bank（BDB）签订了为期两年的货币掉期合同。掉期合同要求ACC以加元（C $）进行半年付款，并以美元（US $）接受半年付款。加元名义金额为2500万加元。假设每年360天，该互换的应计期为180/360。美元兑加拿大元的即期汇率为0.77，加元为ACC的本国货币。 C $ LIBOR和USD LIBOR的期限结构如下：
天C $ LIBOR（％）美元LIBOR（％）
180 0.50 0.55
360 0.60 0.65
540 0.65 0.75
720 0.70 0.85
一个。美元的名义金额是多少？ （1分）
b。计算加元和美元的固定汇率。 （8分）
C。如果掉期条款指定ACC接收固定利率并支付浮动利率，则计算掉期的第一半年付款。 （2分）
d。合同启动时货币掉期的价值是多少？ （1分）
e。假设自签订货币互换合同以来已过240天。新汇率为0.85美元/加元。假设在第180天，180天的加元和美元伦敦银行同业拆借利率保持不变，分别为0.5％和0.55％。在时间240，在给定以下LIBOR期限结构的情况下，计算掉期的价值。（8分）
天C $ LIBOR（％）美元LIBOR（％）
120 0.60 0.60
300 0.70 0.65
480 0.80 0.70
660 0.90 0.80
Question 3. FRA Pricing, Valuation, Payoff, and Hedging (20 marks)
Today is June 1. Sustainable Corporation has an obligation of $25 million coming due on August 1. The company is planning to borrow this amount on August 1 to fulfill its obligation, and plans to pay back the loan on December 1. The company’s borrowing rate is LIBOR + 125 basis points. The company’s bank presents it with the following LIBOR term structure:
# days LIBOR
30 0.90%
60 1.00%
90 1.05%
120 1.10%
150 1.15%
180 1.18%
210 1.20%
240 1.21%
For the calculation of interest, the bank assumes 30 days in a month, and 360 days in a year.
Ms. Devro, the VP Finance of Sustainable, is worried that LIBOR will increase between June and August, thus increasing the company’s borrowing cost. She advises that the company enters into a forward rate agreement (FRA) with its bank to hedge its interest rate risk. She has asked you, the treasurer of the company, to present her with answers to the following questions:
a. Should Sustainable take a long or short position in the FRA? (1 mark)
b. What is the fixed rate on the FRA, based on the LIBOR term structure provided by the bank? (4 marks)
c. July 1 is the end of the company’s third quarter of operations, and the company must estimate the fair value of all its contracts, including derivatives, for its quarterly financial statements. What is the value of this FRA if the LIBOR term structure turns out to be the following on July 1? (5 marks)
# days LIBOR
30 0.90% + 0.50%
60 1.00% + 0.50%
90 1.05% + 0.50%
120 1.10% + 0.55%
150 1.15% + 0.55%
180 1.18% + 0.55%
210 1.20% + 0.60%
240 1.21% + 0.60%
d. What will be the payoff on the FRA on August 1 if the company’s business analysts expect the LIBOR term structure to turn out to be the following when the FRA expires? (3 marks)
# days LIBOR
30 0.90% + 0.50%
60 1.00% + 0.50%
90 1.05% + 0.50%
120 1.10% + 0.55%
150 1.15% + 0.55%
180 1.18% + 0.55%
210 1.20% + 0.60%
240 1.21% + 0.60%
e. Given the LIBOR term structure given for August 1 in Question 3, what are the effective annual rates with and without the FRA hedge? For compounding interest calculations, the company uses 365 days per year. (6 marks)
f. Should Sustainable hedge its interest rate risk with this FRA? (1 mark)
Question 4. Interest Rate Options – Pricing, Valuation, Payoff, and Hedging (20 marks)
Tango Bank has contracted to lend $80 million to Delta Co. in three months’ time. This loan will be for a period of six months. To hedge against the risk of interest rates dropping, Tango has purchased an interest rate put option. The put option has an exercise rate of 2.15% and a maturity of three months. The underlying forward rate is based on the LIBOR, which has a current term structure of
# days LIBOR
90 2%
270 2.3%
The terms of the LIBOR specify 30 days in a month and 360 days in a year. The volatility on the underlying forward rate is 0.25. Tango uses the Black Model to estimate the call premium.
a. Calculate the contract premium the bank must pay for this put option. (7 marks)
b. Suppose that in three months’ time, the six-month LIBOR turns out to be 2%. What is the annualized rate of return on Tango’s position with the put option? (7 marks)
c. Hindsight being 20-20, should Tango have purchased the put option? (3 marks)
d. Tango could also have used a forward rate agreement (FRA) to hedge its future lending rate. What are the similarities and differences between interest rate option and FRA? (3 marks)
Question 5. Delta Hedging (8 marks)
A portfolio consists of 1,000 shares of stock and 500 short calls on that stock. The current stock price is $92.20. The call option has a maturity of one year, with an exercise price of $100 and a standard deviation of 25%. The risk-free rate is 5%. The call option price is found by using the Black-Merton-Scholes model. What would be the dollar change in the value of the portfolio be in response to a one-dollar increase in the stock price?
Question 6. VAR Calculation (12 marks)
A firm has a portfolio composed of stock A and B with normally distributed returns. Stock A has an annual expected return of 15% and annual volatility of 20%. The firm has a position of $100 million in stock A. Stock B has an annual expected return of 25% and an annual volatility of 30% as well. The firm has a position of $50 million in stock B. The correlation coefficient between the returns of these two stocks is 0.3.
a. Compute the 5% annual VAR for the portfolio. Interpret the resulting VAR. (5 marks)
b. What is the 5% daily VAR for the portfolio? Assume 365 days per year. (2 marks)
c. If the firm sells $10 million of stock A and buys $10 million of stock B, by how much does the 5% annual VAR change? (5 marks)