Mathematical Finance Wizardry #Finance

this is a mathematical Finance book it is called an elementary introduction to mathematical text-decoration: none;">Finance options and other topics and it’s by Sheldon Ross Sheldon Ross is a living legend he’s written other books that are awesome and he’s published a lot he’s a professor at Berkeley University in California the audience of this book

is undergraduate students interested in mathematical Finance or professional Traders so if you have an interest in math #1a73e8; text-decoration: none;">Finance or if you’re a professional Trader then this is a book for you let me just warn you though if you’re a professional Trader and you’re interested in this book you know this book is a math book it’s pretty serious and it’s

pretty hardcore so it’s going to take some effort to learn the mathematics in this book here is the copyright Cambridge University press 2003. it’s funny Cambridge University press is the only publishing company to ever contact me and send me a book so they didn’t send me this one

they sent me another book a long time ago but it’s pretty cool pretty good stuff let’s take a quick look at the content so you can see what this book contains so it starts with probability and it assumes no knowledge but we’re going to look at the section so you can see exactly

how challenging it is so you can see if it’s a good book for you normal random variables geometric brownie in motion Interest Rates and Present Value analysis pricing contracts via Arbitrage the Arbitrage theorem and then the Black Shoals formula they do derive the Black

Shoals formula from scratch that is one of the main goals of the book it’s to introduce probability in Finance and general

style="font-weight: bold; color: #1a73e8; text-decoration: none;">Finance topics and then derive the Black Shoals here’s some additional results on options a little bit more advanced stuff really really cool to have a book like this there’s not that many books that are like this so

that makes this book really unique this book is also very clean wait till you see the inside of the book exotic options barrier options Asian and look back options pricing exotic options by simulation and then here are the rest of the contents and you notice that there’s no answers in the

back of the book and I’ve checked I’ve read small portions of this book I’ve looked through it there are no answers there’s just exercises that is probably the biggest biggest Con in this book is that it does not contain answers so it’s not really like a book that you

can buy to like you know do practice problems with but it’s a book to learn mathematical Finance and it’s awesome let’s take a look at the introduction and

preface so you can see how to the point this book is an option gives one the right but not the obligation to buy or sell a security under specified terms a call option is one that gives the right to buy and a put option is one that gives the right to sell the security both types of options will

have an exercise price and an exercise time and then it goes on and talks about the two types of options so European options can be utilized only at the exercise time I remember learning about European options for the first time when when studying uh mathematical

href="https://cashnews.co/finance" style="font-weight: bold; color: #1a73e8; text-decoration: none;">Finance in grad school I never knew what a European option was until I was you know learning this stuff whereas American options these are the ones we see in the U.S Stock

Market can be utilized at any time up to exercise time and then it goes on and you know it really formalizes it thus for instance a European call option with exercise price K and exercise time T gets its hold of the right to purchase at time t one share of the underlying security for the

price K and then the American call option you can do the same thing but at any time before T which is really cool now it says here uh one share of the underlying security it doesn’t quite work that way in practice it’s a little bit different it’s actually a hundred

Shares that’s the way it works at least in the US with American style call options here’s where it gets really interesting so black and Shoals showed under the assumption that prices follow a geometric Brownian motion that there is a single price for a call option that

does not allow an idealized Trader one who can instantaneously make trades without any transaction costs to follow a strategy that will result in a sure Profit in all cases that is there will be no certain Profit it asked no Arbitrage if and only if the price of

the option is as given by the Black Shoals formula that is extremely powerful and I have to mention that black controls they both won the Nobel Prize for coming up with the Black Shoals equation which is pretty amazing it’s such a big result that they were given or awarded the Nobel Prize

here you can see that this is actually a very clean math textbook it’s to the point there is no fluff so it’s laid out like a math textbook and it reads like a math textbook it’s beautiful and again the biggest con of this book is that there are no solutions to the exercises but

you have clean explanations that are correct and I think that makes it worth it one thing I think that people might struggle with is reading this book you know if you don’t have a lot of math background this is a math book right this is definitely not something for beginners Sheldon Ross

indicates in the preface that no previous background of probabilities required and he’s correct right he starts from the very beginning you know he defines here a sample space let’s read the very beginning here consider an experiment and let s call the sample space be the set of all

possible outcomes of the experiment if there are n possible outcomes of the experiment then we will generally number them from 1 through M so s the set containing the numbers 1 through M however when dealing with specific examples we usually give more descriptive names to the outcomes and then it

gives several very very easy examples that you would typically see in for example an introductory course on statistics or probability for example the first example is a simple coin toss with one coin and then here he gives another example of rolling a pair of die so really basic stuff that

you’ll probably see in an intro to statistics course but it goes pretty quickly you can see here on page five we’re already at conditional probability right so in a lot of Statistics books that’s a separate chapter so the pace of this book is very very quick random variables and

expected values again in many statistics books this is a separate chapter Sheldon Ross has it as 1.3 on page nine so you know we’ve we’ve covered nine pages but if you compare it to other books you know you could have traveled you know three or four chapters already in content because

other books will give more examples they’ll have exercises you know this is a little bit more to the point let’s keep going here so you can see some more of the mathematics in this book chapter seven is where he derives the Black Shoals formula here it starts talking about it consider a

call option having a strike price K and expiration time T that is the option allows one to purchase a single unit of an underlying security at time t for the price k then it says suppose further that the nominal interest rate is R compounded continuously and also the price of the security follows a

geometric Brownian motion with drift parameter mu and volatility parameter Sigma then it says under these assumptions we will find the unique cost of the option that does not give rise to an Arbitrage and so let’s skip all of the beautiful math that we have here look at all this mathematics

and basically he’s been building up to this point the whole book right just to give you the background so you can understand the derivation so if you want to understand the derivation of Black Shoals buy this book and here it gives you uh known as the Black Shoals pricing formula and this

this is what gave them the Nobel Prize right they won the Nobel Prize because they came up with this which is pretty awesome I’m getting Goosebumps what an incredible powerful formula the book itself is a really good size like it’s a really nice size you can open it up it’s good

quality The Binding feels tight and the pages seem to be fairly good quality and let me just give it a whiff here just gotta smell it yeah it smells pretty clean it’s a nice clean copy so this is a great book for anyone who again wants to learn mathematical

href="https://cashnews.co/finance" style="font-weight: bold; color: #1a73e8; text-decoration: none;">Finance or is serious about using real mathematics in their trading I recently made a CashNews.co on another book on trading this is mainly a math

style="font-weight: bold; color: #1a73e8; text-decoration: none;">Finance book it’s not really a trading book and I think it’s a great book but it uses something called technical analysis and not everyone agrees with technical analysis because it’s not really mathematics so I

wanted to do another CashNews.co like this one where I show you an actual mathematical Finance book so the biggest problem with this book again is the learning curve right it takes a lot of

time it’s a math book and it’s not a book that you can buy and you’re just gonna like go out and like make tons of money in the Stock Market it’s a math none;">Finance book that’s going to teach you actual mathematical Finance one of the things that always happens when I post CashNews.cos on

href="https://cashnews.co/finance" style="font-weight: bold; color: #1a73e8; text-decoration: none;">Finance is the comment section usually gets attacked by spammers so just be careful if you’re reading the comments and you see stuff about

style="font-weight: bold; color: #1a73e8; text-decoration: none;">Crypto and then like there’s people replying and they all look like oh yeah I tried this Crypto thing it worked

great just be careful with the comments I usually when I see those spammers I report them but I don’t always catch it and I think sometimes YouTube definitely removes comments YouTube YouTube definitely removes comments uh sometimes when they suspect spamming so yeah just watch out and always

remember this when it comes to Finance okay this is really important nobody cares about your money more than you right nobody does nobody does it’s your money you work

hard for it and you don’t want to lose it right so just be careful and just remember that and don’t believe anyone if someone’s out there telling you that they’re going to sell you this program that always works or they have this trading strategy where they’re going to

get rich not true because if it really worked then they wouldn’t be selling their strategy so Pros I would say the pros of this book are that it is super clean right it’s got nice examples it’s got definitions it’s got content that you can’t find in a lot of other

books it’s written by a legendary mathematician Sheldon Ross he is awesome I have several of his other books and I used one of his other books uh when I was in grad school studying stochastic processes so those are all Pros con the book does not have um any answers to the problems that is a

big con and I think that’s kind of a problem in any case I think this book is still worth it for anyone who either wants to learn probability or wants to learn mathematical Finance if

you’re a math major and you have any interest in math Finance get this book it’s probably one of the best ones you can get by the way if you know other good math

href="https://cashnews.co/finance" style="font-weight: bold; color: #1a73e8; text-decoration: none;">Finance books please let me know in the comments I’m curious I have a couple others but I really like this one because of the layout and it’s clean and it’s written by Ross

Ross is really good overall I think this is a solid book on mathematical Finance and I think it’s great for anyone who wants to learn probability and or mathematical

href="https://cashnews.co/finance" style="font-weight: bold; color: #1a73e8; text-decoration: none;">Finance if you want to learn probability using this book I do recommend that you get other books also to help you there’s nothing wrong with using this book to learn probability it’s

just that I feel like you’re going to need some answers to the exercises and maybe some more examples to really really solidify your skills the book by wackerly and mendelhall is a mathematical statistics book which has answers to the odd problems and you can buy a Solutions manual for it so

I’ll leave a link in the description to that book as well as a link to this book as well also Ross has a probability book which is excellent and I’ve already reviewed it so I will leave a link to that one as well so you can get both books by Ross if you really think Ross is the way to

go but yeah great book only only negative is no answers but that’s just something the book doesn’t have right like I can’t really say that anything that the book has is bad so there’s no real negative content in the book it’s all clean it’s all precise it’s

all awesome and it’s all written by a legend Sheldon Ross I definitely like this book and I recommend it I hope this CashNews.co has been helpful and informative if you are still watching this CashNews.co and you are not subscribed to the channel consider subscribing I post book reviews and

all kinds of other types of CashNews.cos until next time good luck take care and be careful Trading