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Mathematics for Finance An Introduction to Financial Engineering [EXP-37269]
192 SOLVED PROBLEMS
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Question: 10.8
A 2-year bond with $100 face value pays a $6 coupon each quarter and has 11% yield. Compute the duration.
Verified Answer:
Formula (10.2) can be applied directly to find D ≅...
Question: 2.34
A bond with face value F = 100 and annual coupons C = 8 maturing after three years, at T = 3, is trading at par. Find the implied continuous compounding rate.
Verified Answer:
Since the bond is trading at par, its initial pric...
Question: 2.1
A sum of $9,000 paid into a bank account for two months (61 days) to attract simple interest will produce $9,020 at the and of the term. Find the interest rate r and the return on this investment.
Verified Answer:
The rate r satisfies
\left(1+\frac{61}{365}...
Question: 6.5
A US importer of German cars wants to arrange a forward contract to buy euros in half a year. The interest rates for investments in US dollars and euros are rUSD = 4% and rEUR = 3%, respectively, the current exchange rate being 0.9834 euros to a dollar. What is the forward price of euros expressed
Verified Answer:
The euro plays the role of the underlying asset wi...
Question: 2.37
After how many days will a bond purchased for B(0, 1) = 0.92 produce a 5% return?
Verified Answer:
The continuous rate implied by the bond satisfies ...
Question: 5.12
Among all attainable portfolios constructed using three securities with expected returns μ1 = 0.20, μ2 = 0.13, μ3 = 0.17, standard deviations of returns σ1 = 0.25, σ2 = 0.28, σ3 = 0.20, and correlations between returns ρ12 = 0.30, ρ23 = 0.00, ρ31 = 0.15, find the minimum variance portfolio. What
Verified Answer:
The weights of the three securities in the minimum...
Question: 5.13
Among all attainable portfolios with expected return μV = 20% constructed using the three securities in Exercise 5.12 find the portfolio with the smallest variance. Compute the weights and the standard deviation of this portfolio.
Verified Answer:
The weights in the portfolio with the minimum vari...
Question: 2.28
An investor paid $95 for a bond with face value $100 maturing in six months. When will the bond value reach $99 if the interest rate remains constant?
Verified Answer:
We solve the equation
100 = 95 (1 + r)^{\fr...
Question: 4.8
Apply the Fundamental Theorem of Asset Pricing to find the time 0 and 1 prices of a put option with strike price $110 maturing after two steps, given the same scenarios ω1, ω2, ω3, ω4, stock prices S(0), S(1), S(2) and money market prices A(0), A(1), A(2) as in Example 4.5.
Verified Answer:
The put option gives the right (but no obligation)...
Question: 11.11
Assume the structure of bond prices in Example 11.5 (Figure 11.10). Consider a coupon bond maturing at time 2 with face value F = 100 and coupons C = 1 payable at each step. Find the price of an American call option expiring at time 2 with strike price X = 101.30. (Include the coupon in the bond
Verified Answer:
At time 2 the option is worthless. At time 1 we ev...
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