Mathematical Techniques in Finance - Amir Sadr

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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

      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.

      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.

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 Скачать книгу