Need a book recommendation to supplement my undergrad class

[yzia]

I'm currently using Sheldon M. Ross's An Elementary Introduction to Mathematical Finance: Options and Other Topics. And to say the least, it sucks. The questions have no solutions to see if you're right and they pertain very little to what you read in the chapter - its as if you read in depth into a specific topic and have to answer questions that are somewhere in the same ballpark (but far away, think upper deck behind home plate and left field). Further, there's no way to tell if you're even in thinking in the right direction, as there are no solutions.

Oh, and each chapter is nary over 8 pages. The professor of my course, though a great guy, teaches straight out of the book, going over Sample Exercises found in the book, copying them down step for step for step. And it's not as though I'm just not getting it - everyone in the class is struggling and I took the initiative (with their support) in finding an alternative.


So I'm looking for a book that will supplement what I'm learning. The book is here: Amazon.com: An Elementary Introduction to Mathematical Finance: Options and other Topics (9780521814294): Sheldon M. Ross: Books

and it covers these topics:

1. Probability;
2. Normal random variables;
3. Geometric Brownian motion;
4. Interest rates and present value analysis;
5. Pricing contracts via Arbitrage;
6. The Arbitrage Theorem;
7. The Black-Scholes formula;
8. Valuing by expected utility;
9. Exotic options;
10. Beyond geometric Brownian motion models;
11. Autoregressive models and mean reversion;
12. Optimization methods in finance.


To give an example of how terrible this book is, the chapter on Brownian Motion goes over the equation and what to plug in where, the questions, as a whole, deal with probabilities of brownian motion, something that the chapter itself does not cover anywhere.

 

[bigbadwolf]

The Ross book sucks, I agree (I have a copy myself). I would recommend Brownian Motion Calculus, by Wiersema, pub. by Wiley. Another book that comes to mind is An Introduction to the Mathematics of Financial Derivatives, by Neftci, pub. by Academic. And I almost forgot Mathematics for Finance, by Capinski and Zastawniak, pub. by Springer (elementary but sound pedagogically).


At a more advanced level I would recommend Introduction to Stochastic Calculus with Applications, by Klebaner (2nd ed.), pub. by Imperial College Press, or the two volumes that comprise Stochastic Calculus for Finance, by Shreve, pub. by Springer.

 

[CGiuliano]

bbw - You seem to have read enough math textbooks to fill a small library. Can you comment on Ross's A First Course in Probability? I have mixed feeling about it. Well, other than the absolutely terrible introduction, I think it gives interesting examples, and is just instructive enough. What do you think?

 

[Sanket Patel]

bbw - You seem to have read enough math textbooks to fill a small library. Can you comment on Ross's A First Course in Probability? I have mixed feeling about it. Well, other than the absolutely terrible introduction, I think it gives interesting examples, and is just instructive enough. What do you think?

In my opinion, the book is a good treatment of combinatorics-based probability. The book contains a lot of good 'brain-teaser' and 'interview' type questions, but I probably wouldn't recommend the book as your 'main' probability book.

I'd recommend 'An Introduction to Probability' by Dmitri Bertsekas and John Tsitsiklis. Also, if you can get used to his style, I'd also recommend David Williams' 'Probability With Martingales' and 'Weighing the Odds'

 

[bigbadwolf]

Can you comment on Ross's A First Course in Probability? I have mixed feeling about it.

It's a standard calculus-based text. It's okay but not inspired. There's no accounting for taste but if I had to recommend a text, it would be Probability for Applications, by Pfeiffer, and published by Springer (out of print, but used copies floating around). I'll come back to this thread later if I can and list some more books that may come to mind. Before I forget, Feller's two books on probability (pub. by Wiley) are classics.

 

[const451]

In my opinion, the book is a good treatment of combinatorics-based probability. The good contains a lot of good 'brain-teaser' and 'interview' type questions, but I probably wouldn't recommend the book as your 'main' probability book.

I'd recommend 'An Introduction to Probability' by Dmitri Bertsekas and John Tsitsiklis.

I second that opinion.

A First Course in Probability by Ross has little theory but a lot of solved problems.

An introduction to probability by Dmitri Bertsekas and John Tsitsiklis, IMO is the best intro to probability, their website contains answers to exercises. It's in 2nd edition.

 

[CGiuliano]

Thanks everyone.

 

[yzia]

The Ross book sucks, I agree (I have a copy myself). I would recommend Brownian Motion Calculus, by Wiersema, pub. by Wiley. Another book that comes to mind is An Introduction to the Mathematics of Financial Derivatives, by Neftci, pub. by Academic. And I almost forgot Mathematics for Finance, by Capinski and Zastawniak, pub. by Springer (elementary but sound pedagogically).


At a more advanced level I would recommend Introduction to Stochastic Calculus with Applications, by Klebaner (2nd ed.), pub. by Imperial College Press, or the two volumes that comprise Stochastic Calculus for Finance, by Shreve, pub. by Springer.

Yeah, I'm liking the Mathematics of Finance book. Do you happen to have this one? If so, would it fill-in as a great supplement to the Ross book?

 

[bigbadwolf]

Yeah, I'm liking the Mathematics of Finance book. Do you happen to have this one? If so, would it fill-in as a great supplement to the Ross book?

I have the book but it's not with me at the moment. As I remember, it doesn't have coverage of stochastic calculus -- which is what Ross is glossing over. The books by Wiersema or Neftci should give you the detailed treatment you need.

The problem is that covering stochastic calculus takes time, effort, patience. There are a lot of subtle details involved. It's difficult to do this if you have to stay abreast of the rubbish being covered in the class at the same time (I've been in the same situation several times, where the instructor was a buffoon and the book was garbage). So perhaps don't look at Wiersema and Neftci as supplements; rather see them as what your instructor shoud have been using in the first place. Ross needs to be supplanted, not supplemented.

Ross has one good book out, which I can unequivocally recommend: his book on simulation. Slim book -- but excellent introduction to Monte Carlo methods, and instructive worked examples.

 

[yzia]

If it makes a difference, here's what the class covers:

1.1) Elementary Probability, Events.
1.2) Conditional Probability, Independence.
1.3) Random Variables and Expectation.
1.4) Covariance and Correlation of Random Variables.
2.1) Continuous Random Variables.
2.2) The Normal Random Variable, Gaussian distribution.
2.3) Properties of Normal Random Variables.
2.4) The Central Limit Theorem.
3.1) Brownian Motion and Geometric Brownian Motion.
3.2) Geometric Brownian Motion as a limit of Simpler Models.
3.3) Brwonian Motion revisited.
4.1) Interest Rates.
4.2) Interest Rates and Present Value Analysis.
4.3) The Rate of Return.
4.4) Continuously Varying Interest Rates.
5.1) Options Pricing.
5.2) Pricing via Arbitrage.
5.3) Examples.
6.1) The Arbitrage Theorem.
6.2) The Multiperiod Binomial Model.
6.3) The Arbitrage Theorem Revisited.
7.1) The Black-Scholes Formula
7.2) Properties of the Black-Scholes Formula
7.3) The Delta Hedging Arbitrage Strategy
7.4) On the Derivation of the Black-Scholes Formula.
8,1) Call Options on Divident-Paying Securities
8.2) Pricing American Put Options
8.3) Adding Jumps to Geometric Brownian Motion
8.4) Estimating the Volatility Parameter
9.1) Arbitrage Pricing Revisited
9.2) Valuing Investments by Expected Utility