Quantitative Financial Analysis Week III Notes
Quantitative Financial Analysis Week III Notes BU.230.710.52.SP16
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This 5 page Class Notes was uploaded by Kwan on Friday April 1, 2016. The Class Notes belongs to BU.230.710.52.SP16 at Johns Hopkins University taught by Stuart Urban in Spring 2016. Since its upload, it has received 68 views. For similar materials see Quantitative Financial Analysis in Finance at Johns Hopkins University.
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Date Created: 04/01/16
Quant III Friday, April 1, 2016 09:03 1.HW2 Right click the function, open the function file .*: in case of vectors Syntax: [B,D]=… More flexible: more variables Use a single variable to store the repeated calculation A = xlsread('xxx','Sheet1'): read all data ID = A(:,1) Max -‐-‐> get vectors 2.Monte Carlo Simulation A series of simulations Central limit theorem: handy -‐-‐> what distribution (what result) not im--t can calculate confidence… B-‐S Model: constant interest rate and constant volatility [not true in reality] -‐-‐> Monte Carlo Eg. Estimating Pi -‐-‐>as a function file: no inputs and outputs (shootingDart: No functions in Script) Formatting: fprintf: format string (&) s: strings; d: integer; %10d\n: new line; matrix: transposed Eg. Integration X = rand(N,1); I= mean(cos(2*pi*X)); Shift + enter: change all names Function inside a script: cannot be used in other scripts MC_estimatePi -‐-‐> MC_estimateInteger (not a function, change only a few lines) Convergence Standard error: SEM Norinv(.975) [5% -‐-‐> 2.5%] file: MC_estimatePi_withError.m 3.BUILDING A STOCK PRICE MOVEMENT PROCESS Noise/random shock/random price shock: ???? ????: only variable, ~N 252: days in US stock market per year S(0) → index 1 in matlab: s(1) = 40; Closse all: close all pups-‐‑ Matlab: 2 lines (Monte Carlo)-‐‑ -‐‑ milion Don't use MC_stockPrice.m -‐‑-‐‑>Ito (log normal) Closse all: close all pups-‐‑ Matlab: 2 lines (Monte Carlo)-‐‑ -‐‑ milion Don't use MC_stockPrice.m -‐‑-‐‑>Ito (log normal) Motivation: our stock prices don't go below zero… 4.OPTIONS PRICING Risk-‐‑Newtral Valuation: No arbitrage oportuinies; Miu=r MC_pricingEUCall.m Drift & diffusion HW3: Don't overthink: change to PUT /butterfly function (payoff) & change nam-s> Done! Cf. Black-‐‑Scholes Pricing Formula (pricing) Normcdf: d1, d2 -‐‑-‐‑ Delta: slope of Call Price vs S0 Gamma: slope of delta Graph -‐‑→ magnifying around 42, the price is 4.76 5.Variance Reduction Techniques Multiple dimensions Random -‐‑→ Quasi-‐‑random Skewed -‐‑→ even out (mean is 0) 5.Variance Reduction Techniques Multiple dimensions Random -‐‑→ Quasi-‐‑random Skewed -‐‑→ even out (mean is 0) 6.Asion Options & tips Path/trajectory Mean -‐‑-‐‑> around T=20, 40, 60, 80, 100 How good the estimate is--‐> standard error (4*std error = range) [1.96] Simulation: don't interact with each other Min? Path-‐dependent option or not? More steps -‐-‐> price: random walk (expect to go up) Payoff: Lower bound, infinity; With K, no cancel out below 0 4 steps per day (in real world) Increment matrix: Adding from 250 -‐-‐>251 (logS0+delta s1 + delta s2: the first column) LogPaths = cumsum([log(S0)*ones(NbTraj,1) , Increments] , 2); :-‐ d own, 2 -‐ cross Cumulative sum [Conclusion: don't touch the GenerePaths function]
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