For the people who'll go to the inspection. Could you keep us posted , especially good for all the next year students. From the little bits we can reconstruct the exam. Maybe this will bring more clarification for the next gen...
For what I can still remember is that:
Q1: Asks about replication/ How to hedge (u and d given)
-Perform a hedge of the underlying future you calculated
Q2: A Deutsche bank case of an investment product, which pays 100 if it is below 100, 100- 120 as it follows the stock index and 120 if the stock index is above 120. (Long put at strike 100 + Short call at 120) then you have to replicate the same thing at the AEX (Dutch index) and talk about the things you had in the last years part 2 exams.
Q3: Calculate implied volatility given a formula
-Perform a delta hedge
What are the shortfalls of using a delta hedge only (transaction costs etc.)
What alternative could you do (Hedging with the greeks, just adjust daily/weekly etc. instead of with every move of the stock (Dynamic hedging)
Hedge gamma neutral BUT you can only choose a strike price which is not equal to 100 (Used for delta) and you have to calculate the price and implied volatility using the given implied volatility formula
This is all assuming constant volatility
Now what would you have to do if you want to hedge and volatility is not constant --> Vega hedge
To perform a vega hedge you would need a third option (Different strike price) and go through the procedure again with calculating the price and implied volatility.
Make sure you know how to calculate the derivate of N'(d1) and N'(d2)
For a) i) B is negative (See volatile smile on equity, it's a decreasing function of the strike price, so as K increase, sigma decreases which means it's coefficient is negative.
Compute the sigma IV with that formula and use that in ii) to compute the price with BS for every option and henceforth for the price of the portfolio.
not sure about iii. , iv. is in the book (hedging continuously is costly, etc....)
This is something similar what the tutor showed last year (although we did not finish it). As for pricing you could argue for either binomial or BS but you would need to mention the required inputs. And some bulls** a la, BS price and binomial are pretty similar a bit of volatility smile etc. However, as I said we did not finish it and the tutor mentioned that most people simply draw a graph.
Question 18.16. I am not sure how to calculate the value at time t=2. The upstate has a payoff of 0.035441 and the downstate 0.118818. p= 0.5726 ;t = 1 and steps =3 --> delta t= 1/3 and r=6 % (r foreign =3% but not needed in this case). Normally I would have to calculate (0.5726*0.035441+(1-0.5726)*0.118818)*e^(-6%*1/3) = 0.069669,while the solution should be 0.0783332. What is my mistake?
It is not needed for discounting, because you can either invest in the product (in this case the Forex option) or put the money in your home country in a risk-free account. However, if you invest in the Forex Option you have to calculate exsactly how much money you will get. Interest rate differentials affect the price. E.g. if you have an exchange rate which is 1:1 and have the same interest rates, then in 1 year if there is no appreciation/depreciation it should be as well 1:1. However, if you have interest rate differentials the (covered/uncovered) interest rate parity will affect the relation. If one country pays 0% interest while the other pays 100%, the no-arbitrage condition should still hold which means that the one which pays 100% interest will loose 50% in value next year.
For the less mathematically blessed among us (me). Wouldn't you usually multiply both sides by the S0. Furthermore, the 40% shift is also not obvious. Would greatly appreciate if you could explain it or point me to the obvious thing I am missing.
To make it easier lets say the e^- stuff is X for the first half and Y for the second half, so the function is 0.4A * 1/s0 *(s0*X - S0*Y) . If you would write it out it would be 0.4*(1/s0 *s0 *x - 1/s0 *s0*Y) And since s0/s0 = 1 we can get rid of it and end up with 0.4*(X-Y)
At Short 350 (e.g. J27) Why is it +$H$11 instead of -$H$11 in the second part of the function? In the first part of the function it is -$H$11 *$E$17 as well. You will still receive the price of the short call no matter if the buyer exercise it later or not???
In the first part they multiply minus number of short# by minus cost of option, thus getting a positive number profit. In the second part they probably counted that the payoff at sufficiently high S will be negative anyway and only multiply by -# to display it. And also cause it wrong. For example at S355. As naked short seller you would have to buy it in the market and sell it at K. (-355+350+13.75)*189= 1658. You still should receive some profit since (S-K)
updated 1 year ago
Let S=355, K=350, C=15 and #=-1
At (S-K+C)*-# = -20
At (-S+K+C)*# = 10
page 198 chapter 9.2 mechanics of options
(355-350;0) --> - max(5;0)
Somehow it only works on the old studydrive, here is the link:
<a href="https://nostalgic.studydrive.net/courses/maastricht-university/options-and-futures/other/fundamentals-of-futures-and-options-markets-2008-prentice-hall-8th-edition/viewfile/414905" target="_blank">https://nostalgic.studydrive.net/courses/maastricht-university/options-and-futures/other/fundamentals-of-futures-and-options-markets-2008-prentice-hall-8th-edition/viewfile/414905</a>