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Advanced Oil and Currency Bond Pricing with Monte Carlo Simulation

This code implements a financial model to price oil and currency bonds using binomial tree and Monte Carlo simulation techniques. It calculates option prices based on various parameters such as strike price, interest rate, volatility, and time to maturity. Key functionalities include price bounds for oil options, lattice generation for currency options, and payoff calculations for Monte Carlo simulations. The code also demonstrates an example of a cash-or-nothing option using graphical representation for better analysis.

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Advanced Oil and Currency Bond Pricing with Monte Carlo Simulation

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  1. HW8

  2. Oil Bond

  3. Oil Bond - code S = 30; r = 0.02; sigma = 0.06; T = 1; N = 10; deltaT = T/N; u = exp( sigma * sqrt(deltaT) ); d = 1/u; p = ( exp( r * deltaT ) - d ) / ( u - d ); for i = 0 : N oilp(i+1) = S * u^(N-i) * d^(i); if oilp(i+1)<25 oilp(i+1) = 25; elseifoilp(i+1)>40 oilp(i+1) = 40; end oilp(i+1) = 1000+( oilp(i+1) -25)*170; end

  4. Oil Bond – code (conti.) for i = N : -1 : 1 for j = 0 : i-1 oilp(j+1) = exp(-r*deltaT) * ( oilp(j+1)*p + oilp(j+2)*(1-p) ); end oillattice(1:i,i) = oilp(1:i); end format short g oilp(1,1) oillattice

  5. Index Currency Option Notes

  6. Index Currency Option Notes - Code S = 102; r = 0.02; sigma = 0.102; T = 1; N = 10; deltaT = T/N; u = exp( sigma * sqrt(deltaT) ); d = 1/u; p = ( exp( r * deltaT ) - d ) / ( u - d ); for i = 0 : N currp(i+1) = S * u^(N-i) * d^(i); if currp(i+1)>169 currp(i+1) = 1000; elseifcurrp(i+1)<84.5 currp(i+1) = 0; else currp(i+1) = 1000-(1000*(169/currp(i+1)-1)) ; end end

  7. Index Currency Option Notes - Code (Conti.) for i = N : -1 : 1 for j = 0 : i-1 currp(j+1) = exp(-r*deltaT) * ( currp(j+1)*p + currp(j+2)*(1-p) ); end currlattice(1:i,i) = currp(1:i); end format short g currp(1,1) currlattice

  8. Monte Carlo Put Option function [ cp, pp, CIc, CIp] = blsMC( S, K, r, T, sigma, NRepl ) nuT = (r - 0.5*sigma^2) * T; siT = sigma * sqrt(T); c_payoffs = exp(-r*T) * max(0, S*exp(nuT + siT*randn(NRepl,1)) -K ); p_payoffs = exp(-r*T) * max(0, K - S*exp(nuT + siT*randn(NRepl,1)) ); [cp, varc, CIc] = normfit(c_payoffs); [pp, varp, CIp] = normfit(p_payoffs); end

  9. Demo S = 50; K = 50; r = 0.1; T = 1; sigma = 0.2; lamda= 1.2; [blsout_c, blsout_p] = blsprice(S,K,r,T,sigma); bls = ones(100) * blsout_p; for i = 1:100 [bitc(i), bitp(i)] = bitprice(S,K,r,T,sigma,i,0); [tric(i), trip(i)] = triprice(S,K,r,T,sigma,lamda,i,0); [MCc(i), MCp(i), temp1,temp2] = blsMC(S,K,r,T,sigma,i*100); CId(i) = temp2(2)-temp2(1); end

  10. Cash or Nothing function [ cp, pp ] = blsMC2( S, K, C, r, T, sigma, NRepl) nuT = (r - 0.5*sigma^2) * T; siT = sigma * sqrt(T); pvC = exp(-r*T) * C; Stock = S*exp(nuT + siT*randn(NRepl,1)); for i = 1:NRepl c_payoffs(i) = 0; p_payoffs(i) = 0; if Stock(i) > K c_payoffs(i) = pvC; elseif Stock(i) < K p_payoffs(i) = pvC; end end [cp, varc, CIc] = normfit(c_payoffs); [pp, varp, CIp] = normfit(p_payoffs); end

  11. Demo S = 50; K = 50; C = 10; r = 0.1; T = 1; sigma = 0.2; NRpel= 10000; for TS = 1:100 [MC1c(TS), MC1p(TS)] = blsMC2(TS,K,C,r,T,sigma,NRpel); End figure; plot(MC1c); hold on; plot(MC1p,'color',[1 0 0.5]); title('Cash or Nothing');

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