Derivatives and Risk Management 28C00400

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4 Replies to “Derivatives and Risk Management 28C00400”

  1. Exam 30.5.2016 [I don’t remember the questions exactly, e.g. all the parameter values that were used like the volatilities and strike prices]

    There are 4 questions, each worth the same amount of points.

    1) Risk free rate, volatility (per year), current share price and strike price are given.
    a) Make a binomial tree for two periods (2 years) and calculate the value of the call option
    b) You are concerned about the long maturity of two years. A trader offers you a 1-year call option with that has the same strike price as in a) combined with a possibility to extend the maturity of the option for the second year for $4 after the first year. What is the fair value of this option?
    c) If the call option is now trading at C [a price that is lower than calculated in a)]. Is there a possibility to do arbitrage. Explain the trades that you would make in this case. Assume the price mismatch corrects itself after the first year.

    2) A bank offers an certificate called Double Up where you invest the current share price (some share price given). This certificate pays 200% of the return of the stock after one year, i.e. if the stock price has risen 4%, you get paid 8% at the end of the year. If the stock price ends up lower than what it is now, you get back the original price of the share. There is also a cap on the return you get at 20% meaning that the certificate will not pay more than a 20% return (so if the share price goes up more than 10% the certificate will still only pay a 20% return, no more). Risk free rate, volatility and current stock price are given.
    a) Present the payoff diagram for the certificate
    b) How would you replicate the payoff from this certificate using other instruments (e.g. stocks, options…)
    c) If the volatility of the stock increases immediately the next day after you have bought the certificate, will the certificate become more or less valuable? Explain without doing calculations.

    3) Risk free rate, current share price, strike price, u and d are given (and share price = strike price).
    a) Make a binomial tree for two periods and calculate the current value of the call option
    b) a bank offers an option called ”digital” on the stock. This option will pay $1 if the share price exceeds the strike price, 0 if it doesn’t after the two periods are up. What is the value of this option at t=0?
    c) A trader offers you a special option on the stock where you pay nothing now, but if the option ends up in the money after the two periods you must pay a price Y in addition to the strike price. Using the calculations from the previous answers (not starting from scratch), calculate the value of Y
    d) For a put option where you pay nothing for the option now but must pay Z after two periods if the put option ends up in the money, calculate the value of Z

    a) The value of a call option increases with volatility and maturity. Does the same apply for a put option? Explain briefly.
    b) A put and call option have the same maturity and strike price and are currently at the money. Which one has a greater value? Explain.
    c) Explain what delta, gamma and vega tell us about the option.

  2. The exam wasn’t too much work if you know your algebra. There wasn’t that much of it. You should be able to calculate replicating portfolios, binomial trees (with several stages and based on standard deviations), put-call parity, convertible debt valuation, etc. E.g. if you are given the values of two pairs of put and call options with different exercise prices and values, you should be able to calculate the risk-free rate and spot price of the underlying. You should know how to do arbitrage pricing.

    So, in effect, if you know how to do most of the exercises from the lecture slides, you’re home-free.

  3. Workload is good for getting a solid grasp of the basics. The amount of content is not overwhelming, the cases and exercises require some work but don’t go far beyond the basics of derivatives pricing. Overall very good course for building the basic intuition of derivatives pricing, workload is slightly higher than your average finance B.Sc course, but definitely lower than most M.Sc level courses.

    For the exam, it makes sense to know your convertibles, warrants and put-call parity well.


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