Mathematical Modeling in Finance with Stochastic Processes
2.2 Multiperiod Binomial Tree Models 2.2 Multiperiod Binomial Tree Models Rating Student: contains scenes of mild algebra or cal ...
82 CHAPTER 2. BINOMIAL OPTION PRICING MODELS Figure 2.2: A binomial tree We model a limited market where a trader can buy or sho ...
2.2. MULTIPERIOD BINOMIAL TREE MODELS 83 (n+ 1,j) and (n+ 1,j+ 1) at the next trading time, with the “up” change corresponding t ...
84 CHAPTER 2. BINOMIAL OPTION PRICING MODELS 2.3 Pricing a European call ...
2.2. MULTIPERIOD BINOMIAL TREE MODELS 85 2.4 Pricing a European put ...
86 CHAPTER 2. BINOMIAL OPTION PRICING MODELS 7.7 Limitations of the Black-Scholes Model The disadvantages of the binomial model ...
2.2. MULTIPERIOD BINOMIAL TREE MODELS 87 from scratch because the parameters have special and more restricted inter- pretations ...
88 CHAPTER 2. BINOMIAL OPTION PRICING MODELS the value of such a cash-or-nothing binary option with payoff $100 at expiration 2 ...
Chapter 3 First Step Analysis for Stochastic Processes 3.1 A Coin Tossing Experiment Rating Everyone: contains no mathematics. S ...
3 First Step Analysis for Stochastic Processes We callruinthe state of going broke before reaching a fortune goal. Mathematica ...
3.1 A Coin Tossing Experiment 3.1 Welcome to my casino! by recording the flip number, the outcome as “H” or “T” and keeps track ...
92 CHAPTER 3. FIRST STEP ANALYSIS FOR STOCHASTIC PROCESSES 3.2 Welcome to my casino! Tossn 31 32 33 34 35 36 37 38 39 40 H or T ...
3.1. A COIN TOSSING EXPERIMENT 93 Tossn 71 72 73 74 75 76 77 78 79 80 H or T Yn= +1,− 1 Tn= ∑n i=1Yi Tossn 81 82 83 84 85 86 87 ...
94 CHAPTER 3. FIRST STEP ANALYSIS FOR STOCHASTIC PROCESSES Problems to Work for Understanding How many heads were obtained in y ...
3.2 Ruin Probabilities Section Starter Question What is the solution of the equation xn = axn− 1 where ais a constant? What kind ...
96 CHAPTER 3. FIRST STEP ANALYSIS FOR STOCHASTIC PROCESSES Theorems about Ruin Probabilities Consider a gambler who wins or lose ...
3.2. RUIN PROBABILITIES 97 Note that we can rewrite the difference equations as pqT 0 +qqT 0 =pqT 0 +1+qqT 0 − 1. Then we can re ...
98 CHAPTER 3. FIRST STEP ANALYSIS FOR STOCHASTIC PROCESSES (Check for yourself that with this expression 0≤qT 0 ≤1 as it should ...
3.2. RUIN PROBABILITIES 99 Then add these together,and after some algebra, the total is 1. (Check it out!) Forp= 1/2 =q, the pro ...
100 CHAPTER 3. FIRST STEP ANALYSIS FOR STOCHASTIC PROCESSES Corollary 3.The probability of ultimate ruin of a gambler with initi ...
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