Summer 2023

FAQ

1. We know that various social and natural events influence the status of the financial markets. So, an investor tries to link most of the fluctuations in the market with some events for anticipating future asset prices. In view of this, why should one care about a stochastic model of asset price fluctuations?
   It is true that in many cases, a specific event occurs beyond any anticipation, and so the exact occurrence of the resulting shocks in financial assets is not predictable. However, since an asset price gets affected regularly by some events or the other, an empirical distribution of the shocks can be obtained and is meaningful. This distribution/law is more robust than the realizations of an individual one and this does not alter frequently. So, the mathematical modeling of the conditional distribution of future asset prices is relevant when we need to manage risk over a period longer than the immediate future. On the other hand, we recall that for a sufficiently liquid asset, the price changes every hour, without a need for an event to occur. So, a complete knowledge of the events and news is not enough for predicting asset movements. So, the risky assets do have inherent uncertainty in their prices. Hence, a stochastic model becomes relevant.
   There are two types of models of asset price dynamics. One is econometric another is mathematical. An econometric model relies on the history of the immediate past and predicts a range of possible values of the asset price for the next time interval with a certain level of confidence. This is basically a time-series model and is based on statistics. Due to some of their complex structure and the presence of many calibrated parameters, these are believed to have predictive power over a short period. However, these cannot factor in relatively rare events. A mathematical model on the other hand does not attempt to predict tomorrow's asset price. This rather assumes that asset prices are not predictable and uncertainties are inherent. Instead of predicting the realization of the asset price, a stochastic differential equation models the conditional law of the price dynamics. In other words, it is designed to answer only the following question. "If the price at any future time is treated as a random variable, what is its conditional distribution given the past realization of the asset price?" 

2.  Why should one be interested in modeling the conditional distribution of asset price?
   In the financial market, many types of assets are traded. Prices of some secondary risky assets depend on the present anticipation of future distribution of a primary risky asset. For finding a rational price of such secondary assets it's important to have a Mathematical model of the corresponding primary asset. These secondary assets are useful in managing risks.

3. I am reading a paper and I do not fully understand this. I need help in finding some appropriate material so that I am able to completely understand.
   Please contact me to schedule a class where you will present the concepts of the paper in simple terms to everyone and then place your question. If anybody else has also read that part and has similar or other doubts on that paper may also mention those. We will have a discussion following that.

4. I am not familiar with the concepts of Black Scholes's option pricing theory. What should I read to get a working knowledge?
   Read sequentially 

   1. https://en.wikipedia.org/wiki/Stock 

   2. https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1997/press.html 

   3. https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model

5. I am willing to learn the subject of math finance beyond the scope of this summer school. I am seeking guidance on how to start with.
   Check this link. You may find these references useful.

6. I wish to learn more about the use of simulation for finding the theoretical price of options. How should I start?
   Read this report made by some earlier students.

7. I wish to learn some fundamentals of simulation techniques quickly. How should I start?
   Read this report made by some earlier students.