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 losspresent valueYTMyield to maturityp.a.per annumdiscount factor, today's value unit payment at future date dicount factor at for unit payment at interest ratecompounding interest rate with compoundings per yearyieldAPRannual percentage rate – stated interest rate without any compoundingsAPYannual pecentage yield – yield of a deposit taking compoundings into consideration: for compoundings per yearCFcash flowcoupon rateprice of an ‐year bond with coupon rate , paid times per year, with yield accrual fraction between 2 dates according to some day count basisclean price of a bond = Price accrued interestprice of an ‐year zero‐coupon bond with yield , compoundings per yearprice 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 annuitybalance of a level pay loan after periodsprincipal and interest payments of a level pay loan in the th periodprice of ‐year level pay loan with loan rate of , paid times per year, with yield ALaverage lifebalance of a level pay loan after periods with prepaymentsprincipal and interest payments of a level pay loan within the th period with prepaymentsSMMsingle monthly mortality rateCPRconstant prepayment ratioperiodic prepayment speedutility of wealth