Today is the big day, the exam is here! Last weeks we have been studying Hull’s book on futures, options and other derivatives preparing for this day. I am hoping the students do well on the exam. A lot of hard work went in to preparation for this one day.
Student are always very anxious to find out how they did on an exam. Therefor we are posting both the exam and solutions here so students can find out how they did. I would like to thank Anne for providing worked solutions to the questions.
For the rest of the world, you are welcome to try the exam and see how you do. If you do run into any problems let us know.
With mix emotions we started the last session of the AG8 series yesterday. It was nice to complete the series, just feels good to get stuff done. On the other hand this was the very last session ever! The course is being integrated in the new curriculum of the Actuarieel Genootschap and will cease to exist in its current form.
The session was focussed on getting the students ready for the up coming exam(s). No new material was presented. We revisited some topics by popular demand. To be well prepared we picked an exam from a previous year and completed the questions as a group.
In Utrecht this week the AG8 group got together to look at applications of the theory that we have built up over the last 6 weeks.Last week the students were asked to put theory to practice themselves, this week they could sit back and relax... a bit.
The cases we covered were based on actual client cases we came across. Having completed cases allows us to use more sophisticated models. We used our time to understand the results and consider what the consequences for pension funds and insurers were.
First we considered a case where a pension fund wanted to hedge their interest rate and stock market risk. Next we had a look at hedging the risks in the guarantee product of an insurer. I did manage to sneak in a little bit of new theory, for details check the attached slide.
Want to know more about guarantees? Check these two links I found them very useful preparing for this talk.
This week it was time for my favourite AG8 session: the case study. This session is all about getting the students from theory into practice. The case requires students to make payoff diagrams, valuations of option structure, compute Greeks and hedge their position. In short all the material we have gone through over the last 5 weeks needs to be used.
The last part of the lecture we looked how pension funds can hedge their interest risk using swaps and swaptions using a stylised model. This is an important bit of the course, since it is my hope that students take these ideas form the classroom to their organisations (often pension funds or insurers).
Black, Scholes and Merton’s famous option price formula wasn’t a new discovery, as shown in the next section. The formula was well know at the time and widely used in the option market. Often it is noted that option trading took off after the publication of the Black-Scholes formula, but this simply is not true... however, the reverse is. In 1973 the Chicago Board Options Exchange (CBOE) opened for business as the first option exchange in the world, making options widely available. This and the introduction of handheld calculators, to do the necessary computations for Black and Scholes, made the formula a success. The formula may not have been a break through, but the way it was derived certainly was. Using the risk free portfolio was the step that made the known formula acceptable to academia. The derivation of the formula is the topic of this note based on research I did for the AG8 lessons on derivatives. Continue reading →
Taylor expansion and Ito calculus are two very important tools for the financial engineer. In this week’s AG8 session, already number 5, we’ll put both to work. First we will use Ito calculus to derive the Black, Scholes and Merton partial derivative equation. Next will skip ahead and look at the famous Black and Scholes option pricing formulae for european puts and calls. Continue reading →
In 1973 the Chicago Board Options Exchange (CBOE) opened for business as the first option exchange in the world. The exchange standardised contract sizes and their underlying. For the first time it was easy to buy and sell call options. Later, in 1977, put options were offered for the first time, making a wide range of option strategies available Continue reading →
The AG8 curriculum considers option valuation methodologies, in particular the Black Scholes and binomial tree. There are many steps needed to derive these models. In preparation for teaching the next class on the binomial tree model, I thought it would be useful to share my notes. Continue reading →
The third AG8 session of a series of eight covered swaps and options. Two very important instruments in the course. Swaps are mainly used for hedging interest rate positions. In the Netherlands this is very relevant for pension funds and insures. There is a lot of political debate on how pension funds dealt with the financial crisis. In this session we studied swaps as an financial instrument hinting how they could be used to reduce risk in pension funds. Later in the course we’ll get it to this topic in more detail. Continue reading →
On Thursday evening the AG8 group got together for the second session of the AG8 derivatives course. Last session we looked at interest rates, cash deposits and bonds. This week we added forwards and futures as new instruments; the first actual derivatives! Continue reading →