Mathematical Techniques in Finance. Amir Sadr

to them. All exercises can be solved by using a spreadsheet package like Excel. The Python projects are longer problems and can be done by small groups of students as a term project.

      It is my hope that by the end of this book, readers have obtained a good toolkit of mathematical techniques, methods, and models used in financial markets and products, and their interest is piqued for a deeper journey into quantitative finance.

      —Amir Sadr

      New York, New York

      December 2021

Acknowledgments

      One learns by teaching and I have learned much from my students at NYU. Many thanks to all of my students over the years who have asked good questions and kept me on my toes.

      Thanks to my editors at John Wiley & Sons: Bill Falloon, Purvi Patel, Samantha Enders, Julie Kerr, and Selvakumaran Rajendiran for patiently walking me through this project and correcting my many typos. All remaining errors are mine, and I welcome any corrections, suggestions, and comments sent to [email protected].

      A.S.

About the Author

      Amir Sadr received his PhD from Cornell University with his thesis work on the Foundations of Probability Theory. After working at AT&T Bell Laboratories, he started his Wall Street career at Morgan Stanley, initially as a Vice President in quantitative modeling and development of exotic interest rate models, and later as an exotics trader. He founded Panalytix, Inc., to develop financial software for pricing and risk management of interest rate derivatives. He was a Managing Director for proprietary trading at Greenwich Capital, Senior Trader in charge of CAD exotics and USD inflation trading at HSBC, the COO of Brevan Howard U.S. Asset Management in the United States, and co‐founder of Yield Curve Trading, a fixed income proprietary trading firm. He is currently a partner at CorePoint Partners and is focused on crypto and DeFi.

Acronyms

bpbasis points, 1% of 1%, 0.0001

future valueIRRinternal rate of returnPnLprofit and loss

present valueYTMyield to maturityp.a.per annum

discount factor, today's value unit payment at future date

dicount factor at

for unit payment at

interest rate

compounding interest rate with

compoundings per year

yieldAPRannual percentage rate – stated interest rate without any compoundingsAPYannual pecentage yield – yield of a deposit taking compoundings into consideration:

for

compoundings per yearCFcash flow

coupon rate

price of an

‐year bond with coupon rate

, paid

times per year, with yield

accrual fraction between 2 dates according to some day count basis

clean price of a bond = Price

accrued interest

price of an

‐year zero‐coupon bond with yield

,

compoundings per year

price of an

‐year annuity with annuity rate of

, paid

times per year, with yield

price of

‐maturity Treasury Bill with discount yield

PV01present value change due to an ”01” bp change in yieldPVBPpresent value change due to a 1 bp change in coupon, present value of a 1 bp annuity

balance of a level pay loan after

periods

principal and interest payments of a level pay loan in the

th period

price of

‐year level pay loan with loan rate of

, paid

times per year, with yield

ALaverage life

balance of a level pay loan after

periods with prepayments

principal and interest payments of a level pay loan within the

th period with prepaymentsSMMsingle monthly mortality rateCPRconstant prepayment ratio

periodic prepayment speed

utility of wealth