# Questions tagged [homework]

Homework questions for students studying Quantitative Finance or a similar subject.

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### One Period Risk Neutral Probability for Caplet

I am studying some financial modeling put together by the Society of Actuaries in the USA. In it, the following practice problem was given: Find the Risk Neutral price of an at-the-money interest ...
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### Replicating call option in market which only trades stock and forward contracts

I am having a bit of trouble with a problem I've been given. Consider a market which only trades a stock and forward contracts. There's only time 0 and 1. Initial stock price S_0 is 10, the forward ...
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### Bjork exercise 7.6: Claim that depends on $T_1$ and $T_0$

See the solution to Exercise 7.6 here. The solution calculates $E^Q (S(T_1)/S(T_0))$ and then just plugs that into the risk neutral valuation formula. But why? The risk neutral valuation formula ...
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$$Z(t) = \exp (a W(t))$$ I am asked to find $dZ$. I am pretty sure it can be done using Ito's lemma. But in all my textbook (Bjork) examples Ito's lemma is giving from a $... 1 vote 0 answers 67 views ### Arbitrage and completeness in multiperiod model? Given a 2-period market with above stock price process along with a riskfree stock with a return of 5%, how do I determine whether the market is arbitrage-free and complete when I only have knowledge ... • 11 1 vote 1 answer 74 views ### construct portfolio offering risk free profit Have trouble understanding this question, seems quite open ended. Assume that$S(0)$is the current rate of exchange for foreign currency. Assume that and$K_n$and$K_f$are rates of return on home ... • 432 2 votes 1 answer 305 views ### Coupon bond pricing problem with reinvestment The three year bond has face value USD 100, and pays USD 5 coupons annually, the last one at maturity. Assume that the continuously compounding rate is 7%. (a) Find the price of this bond. (b) ... • 203 3 votes 2 answers 372 views ### Is there an efficient method or technique to find an arbitrage between two FX dealers? Crossposted on Mathematics SE I was able to solve the following problem and find the arbitrage but only after spending a long time on it and trying out different possibilites. Is there a method or ... • 203 1 vote 0 answers 232 views ### School project about Black Scholes with stochastic volatility In a university project I am looking at Black Scholes model with a stochastic volatility. I’m still not quite sure about my focus (I am in the beginning 'Idea phase'). I want to explain the theory ... • 1,667 6 votes 1 answer 239 views ### 12-month rate calculation for Problem 4.23 in Hull's Options, Futures, and Other Derivatives From Hull's Options, Futures, and Other Derivatives, 8th ed., problem 4.23: Excerpt from Problem 4.23 The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0 ... Calculate the six-... • 165 1 vote 0 answers 121 views ### Need help understanding basics of cash flow engineering I'm studying Financial Engineering, a subject I'm completely new to. I'm using Principles of Financial Engineering 3rd Edition and trying to solve the exercises ... • 121 1 vote 1 answer 221 views ### Asset Liability Management Test Topic Interpretation I will write a test based on Excel and one of the topics is "The Asset Liability related analysis: including the input assumptions generation, constraints, portfolio optimization analysis and results ... • 63 1 vote 0 answers 275 views ### What is the arbitrage opportunity in Arrow-Debreu One Period market Model The one period market model is made of 4 securities(A, B, C, D) and has 4 future states. Assume the market model is complete. and the state prices are (-2, 2, 4, 8). Given that I dont know the payoff ... • 11 2 votes 1 answer 165 views ### Pricing options with two assets I'm studying for a test and am stuck on this practice question: With interest rates equal to 0, two different stocks$S_1$and$S_2$, both valued at \$1 today, can be worth \$2 or \$0.50 at some ...
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Assuming I have a dividend paying asset $S$ with dividend process $D$. Now I would like to use the bank account process $B$ as numeraire and determine the dynamics of $S$ under the the corresponding ...