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Pricing, Modeling
VaR of simulation of delta instruments deviates from the delta normal model
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<blockquote data-quote="quantdaddy" data-source="post: 246961" data-attributes="member: 40504"><p>Hi. I am trying to understand why the value at risk from my simulation deviates from the value at risk based on the delta-normal model in which the 1 % VaR can be calculated as -2.33 * sqrt(delta^2*sigma^2).</p><p></p><p>The instrument is a european put option deep in the money. S_0 = 100, K=10000, T=1/365, r=0.04, sigma = 0.2 which can be priced with the black scholes model. The delta is -1 which is obtained from the black scholes model.</p><p></p><p>From my simulation i get a 1 % VaR of 2.419 and from the delta normal model I get 0.465.</p><p></p><p>The simulation is based on a geometric brownian motion to generate scenarios.</p><p>S_t = S_0 exp((mu-sigma^2/2)*t + sigma * W_t)</p><p></p><p>Does anybody have an idea as to what goes wrong?</p></blockquote><p></p>
[QUOTE="quantdaddy, post: 246961, member: 40504"] Hi. I am trying to understand why the value at risk from my simulation deviates from the value at risk based on the delta-normal model in which the 1 % VaR can be calculated as -2.33 * sqrt(delta^2*sigma^2). The instrument is a european put option deep in the money. S_0 = 100, K=10000, T=1/365, r=0.04, sigma = 0.2 which can be priced with the black scholes model. The delta is -1 which is obtained from the black scholes model. From my simulation i get a 1 % VaR of 2.419 and from the delta normal model I get 0.465. The simulation is based on a geometric brownian motion to generate scenarios. S_t = S_0 exp((mu-sigma^2/2)*t + sigma * W_t) Does anybody have an idea as to what goes wrong? [/QUOTE]
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VaR of simulation of delta instruments deviates from the delta normal model
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