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To determine a set of consistent notations for the book is important. This book is about Financial Models. Appropriate choice of notations would enable the unambiguous specifications of the models and provide clarity to the readers. However, to determine such a set of notations is particularly challenging for this book. The financial models cover the capital markets and corporate finance. In each sub-field of finance, there are standard notations and therefore finding consistency across these sub-fields can be complex.

To accomplish this task, our choice of notations follows some guidelines stated below.

  1. Maintain the accepted notations in the standard literature as much as possible.
  2. Use capital letter to denote securities or present values of cash flows, with subscript u and d denoting upstate and downstate respectively.
  3. gif denotes the period and gif the state of the world
  4. time is denoted by gif or gif , gif , gif . gif or n denote the calendar time as time passes. gif is the maturity date or the expiration date in calendar time. gif is the time-to-maturity
  5. gif is capitalization of the firm or the stock price
  6. gif is a forward contract or futures contract at time gif state gif , expiring at calendar time gif , delivering a zero coupon bond with the time-to-maturity gif .
  7. gif denotes the gif period, gif state, time-to-maturity gif bond i.e., the discount function at the node gif . The par value is $1.
  8. gif is a default free bond that may have coupon at node gif with a maturity date gif . gif is the default free bond that has a maturity gif . The par value is $100.
  9. gif is the default bond with maturity date at gif . The convention is similar to gif .
  10. gif is the firm value or project value
  11. gif is the call option with expiration date gif .
  12. gif is the put option
  13. gif is an asset
  14. gif is a liability
  15. gif is a fixed asset
  16. gif is cash flow, gif is free cash flow, gif is net cash flow,
  17. gif is the yield of a zero-coupon bond with maturity gif at node gif . Hence it is the yield curve or the transfer pricing curve. gif is continuously compounding rate. gif is semi-annual compounding risk-free rate. gif is the one period risk-free rate.
  18. gif and gif denote the foreign risk-free interest rate and the domestic risk-free interest rate, respectively. 
  19. gif and gif denote the spot exchange and the forward exchange rate, respectively.
  20. gif is the yield of a zero-coupon bond, which is not a benchmark representing time value.
  21. gif is the fixed cost
  22. gif is for margins, like profit margin, or the number of sub-periods
  23. gif is for premiums, like default premium, risk premium
  24. gif is for tax rate with subscripts denoting the type of taxes.
  25. gif is the risk neutral probability
  26. gif is the market probability
  27. gif denotes volatilities.
  28. gif is the variance-covariance matrix
  29. gif is the correlation matrix
  30. gif is the cumulative normal distribution function with mean zero and standard deviation 1.
  31. gif is random error or noise
  32. gif is the normal distribution over an (infinitely) short time gif , with mean zero and standard deviation gif
  33. bold letter represents vector
  34. gif : the tilde letters mean the stochastic movement
  35. gif : the bar letters mean the expected value
  36. Euclid font type is used for book values

 

 

 

 

 

 

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