This book is an outgrowth of notes compiled by the author while teaching courses for undergraduate and masters/MBA finance students at Washing-ton University in St. Louis and the Institut ffir HShere Studien in Vienna. At one time, a course in Options and Futures was considered an advanced finance elective, but now such a course is nearly mandatory for any finance major and is an elective chosen by many non-finance majors as well. Moreover, students are exposed to derivative securities in courses on Investments, International Finance, Risk Management, Investment Banking, Fixed Income, etc. This ex-pansion of education in derivative securities mirrors the increased importance of derivative securities in corporate finance and investment management.
part i introduction to option pricing
1 asset pricing basics
1.1 fundamental concepts
1.2 state prices in a one-period binomial model
1.3 probabilities and numeraires
1.4 asset pricing with a continuum of states
1.5 introduction to option pricing
1.6 an incomplete markets example
problems
2 continuous-time models
2.1 simulating a brownian motion
2.2 quadratic variation
2.3 it6 processes
2.4 it6's formula
2.5 multiple it5 processes part i introduction to option pricing
1 asset pricing basics
1.1 fundamental concepts
1.2 state prices in a one-period binomial model
1.3 probabilities and numeraires
1.4 asset pricing with a continuum of states
1.5 introduction to option pricing
1.6 an incomplete markets example
problems
2 continuous-time models
2.1 simulating a brownian motion
2.2 quadratic variation
2.3 it6 processes
2.4 it6's formula
2.5 multiple it5 processes
2.6 examples of it6's formula
2.7 reinvesting dividends
2.8 geometric brownian motion
2.9 numeraires and probabilities
2.10 tail probabilities of geometric brownian motions
2.11 volatilities
problems
3 black-scholes
3.1 digital options
3.2 share digitals
3.3 puts and calls
3.4 greeks
3.5 delta hedging
3.6 gamma hedging
3.7 implied volatilities
3.8 term structure of volatility
3.9 smiles and smirks
3.10 calculations in vba
problems
4 estimating and modelling volatility
4.1 statistics review
4.2 estimating a constant volatility and mean
4.3 estimating a changing volatility
4.4 garch models
4.5 stochastic volatility models
4.6 smiles and smirks again
4.7 hedging and market completeness
problems
5 introduction to monte carlo and binomial models
5.1 introduction to monte carlo
5.2 introduction to binomial models
5.3 binomial models for american options
5.4 binomial parameters
5.5 binomial greeks
5.6 monte carlo greeks i: difference ratios
5.7 monte carlo greeks ii: pathwise estimates
5.8 calculations in vba
problems
part ii advanced option pricing
6 foreign exchange
6.1 currency options
6.2 options on foreign assets struck in foreign currency
6.3 options on foreign assets struck in domestic currency
6.4 currency forwards and futures
6.5 quantos
6.6 replicating quantos
6.7 quanto forwards
6.8 quanto options
6.9 return swaps
6.10 uncovered interest parity
problems
7 forward, futures, and exchange options
7.1 margrabe's formula
7.2 black's formula
7.3 merton's formula
7.4 deferred exchange options
7.5 calculations in vba
7.6 greeks and hedging
7.7 the relation of futures prices to forward prices
7.8 futures options
7.9 time-varying volatility
7.10 hedging with forwards and futures
7.11 market completeness
problems
8 exotic options
8.1 forward-start options
8.2 compound options
8.3 american calls with discrete dividends
8.4 choosers
8.5 options on the max or min
8.6 barrier options
8.7 lookbacks
8.8 basket and spread options
8.9 asian options
8.10 calculations in vba
problems
9 more on monte carlo and binomial valuation
9.1 monte carlo models for path-dependent options
9.2 binomial valuation of basket and spread options
9.3 monte carlo valuation of basket and spread options
9.4 antithetic variates in monte carlo
9.5 control variates in monte carlo
9.6 accelerating binomial convergence
9.7 calculations in vba
problems
10 finite difference methods
10.1 fundamental pde
10.2 discretizing the pde
10.3 explicit and implicit methods
10.4 crank-nicolson
10.5 european options
10.6 american options
10.7 barrier options
10.8 calculations in vba
problems
part iii fixed income
11 fixed income concepts
11.1 the yield curve
11.2 libor
11.3 swaps
11.4 yield to maturity, duration, and convexity
11.5 principal components
11.6 hedging principal components
problems
12 introduction to fixed income derivatives
12.1 caps and floors
12.2 forward rates
12.3 portfolios that pay spot rates
12.4 the market model for caps and floors
12.5 the market model for european swaptions
12.6 a comment on consistency
12.7 caplets as puts on discount bonds
12.8 swaptions as options on coupon bonds
12.9 calculations in vba
problems
13 valuing derivatives in the extended vasicek model
13.1 the short rate and discount bond prices
13.2 the vasicek mode]
13.3 estimating the vasicek model
13.4 hedging in the vasicek model
13.5 extensions of the vasicek model
13.6 fitting discount bond prices and forward rates
13.7 discount bond options, caps and floors
13.8 coupon bond options and swaptions
13.9 captions and floortions
13.10 yields and yield volatilities
13.11 the general hull-white model
13.12 calculations in vba
problems
14 a brief survey of term structure models
14.1 ho-lee
14.2 black-derman-toy
14.3 black-karasinski
14.4 cox-ingersoll-ross
14.5 longstaff-schwartz
14.6 heath-jarrow-morton
14.7 market models again
problems
ppendices
a programming in vba
a.1 vba editor and modules
a.2 subroutines and functions
a.a message box and input box
a.4 writing to and reading from ceils
a.5 variables and assignments
a.6 mathematical operations
a.7 random numbers
a.8 for loops
a.9 while loops and logical expressions
a.10 if, else, and elseif statements
a.11 variable declarations
a.12 variable passing
a.13 arrays
a.14 debugging
b miscellaneous facts about continuous-time models
b.1 girsanov's theorem
b.2 the minimum of a geometric brownian motion
b.3 bessel squared processes and the cir model
list of programs
list of symbols
references
index
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