Binomial Option Pricing: I
Binomial Option Pricing: I premium 8 6078 0 18 6020 124 probability Let’s have a look at put-call-parity The key is the put option Aput option with a strike
The binomial tree model: a simple example of pricing nancial
(a) Probability in the binomial model Denote the risk neutral probability as pfor rising, and 1 pfor falling In an arbitrage-free market the increase in share values matches the (riskless) increase from interest This corresponds to the mathematical expression px0(1 + 10 ) + (1 p)x0(1 10 ) = x0(1 + 5 ):
CH 5: Discrete Probability Distributions
is a binomial distribution EX 6 Selecting random multiple choice with 10 questions, each question has 4 possible answer This is also a binomial distribution 2 Binomial Distribution Formula Given a binomial distribution with ntrials and success probability p, then the probability of xsuccesses is (called binomial probability function) f(x) = n x
73 (a) Find the probability using the binomial distribution
probability that a single billet is longer than 96 5 inches, then use the binomial distribution (b) Determine the probability that 19 or fewer are have a length less than 96 5 inches (c) Determine the probability that all 20 billets are between 96 0 and 96 5 inches 5 16♥ It is known that 20 of all credit applicants have poor credit ratings
Lecture 6: Option Pricing Using a One-step Binomial Tree
Justification of R-N probability • Any portfolio consisting of stock and option with value at T • If the portfolio is perfectly hedged, the above is the same in both states, because of no-arbitrage, we must have • The right-hand-side can be written as for any probability measure
Discrete Probability Distributions and Expectation
Binomial Probability The probability of getting two 6’s in roll a balanced die 5 times experiment is P(2 S’s) =() x (1/6) x (5/6)3 = 5/(23) x (1/6)2 x (1 – 1/6)3 5 2 17 Binomial Probability Model In a binomial experiment involving n independent and identical Bernoulli trials each with probability of success p, the probability of
THE PROBABILITY OF EVENTUAL RUIN IN THE
THE PROBABILITY OF EVENTUAL RUIN IN THE COMPOUND BINOMIAL MODEL BY ELIAS S W SHIU University of Manitoba, Canada ABSTRACT This paper derives several formulas for the probability of eventual ruin in a discrete-time model In this model, the number of claims process is assumed to be binomial The claim amounts, premium rate and initial surplus
DISTRIBUTIONS FOR ACTUARIES
by expositors of probability and mathematical statistics Probability spaces are denoted by upper-case Greek letters and probability events are denoted by upper-case Roman letters The probability of a general random-variable-related event is usually denoted by Pr{z} As usual, cumulative probability functions are denoted by F(z) and probability
Risk-Neutral Probabilities
−1=2 60 with probability 0 5, or 0 976086 0 947649 −1=3 00 with probability 0 5 True Expected Returns Why might the longer zero have a higher expected return? –Investors have short-term horizons, and dislike the price risk of the longer zero –Investors require a premium to hold securities that covary positively with long bonds
Testing Probability Calibrations
Testing Probability Calibrations Abstract Probability calibration is the act of assigning probabilities to uncertain events We develop a testing procedure consisting of two components to check whether the ex-ante probabilities are in line with the ex-post frequencies The rst component tests the level of the probability calibration under
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