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time value of option proportional to sqrt(time)

Vol scales with the square root of time (i.e. variance is linear in time), therefore the value of an option diminishes with it too.
user68819's user avatar
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Quantifying Costs/Benefits Of Partial Hedging

One approach I would take is to plot %hedging v/s PnL variance. A perfect hedge should leak no PnL, and a naked position would have variance of the spot. So you have a downward, convex curve that ...
Arshdeep's user avatar
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Proof of the value of an option using hedging and no-arbitrage [ Paul Wilmott Chapter 3.12.2]

it seems that I did not really understand the meaning of no-arbitrage and risk-free portfolio mean. If I assume no-arbitrage and risk-less, similar to Binomial asset model, the portfolio at time $t$ ...
Ricky Pang's user avatar
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Negative Dupire Variance

What data are you using? Local volatility requires an arbitrage-free implied volatility surface. In general, equities rarely satisfy these conditions on their options because their bid-ask spreads are ...
THATS MY QUANT MY QUANTITATIVE's user avatar
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Proof of the value of an option using hedging and no-arbitrage [ Paul Wilmott Chapter 3.12.2]

Going to go out on a limb here - without having done the maths, isn't the point of his argument that the constructed portfolio is riskless (locally). Therefore, in the next time step it can only earn ...
user68819's user avatar
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Expectation of average, conditional on terminal value

My attempt at an answer (as I've said in the comments, I'm quite rusty... any corrections are appreciated) We have $S_0 > 0$, and since we know $S_T$ we know $\sigma \sqrt{T-t}W_T = b$ for some $b \...
Rylan's user avatar
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7 votes

Preferred Option pricing model

General Comment: In industry, you're effectively an engineer/mechanic. You choose the best tool for the job, and there is no 1 tool that works with everything because they all have different benefits ...
THATS MY QUANT MY QUANTITATIVE's user avatar
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stdev of delta hedged portfolio for call option !=0. Why?

Seems like I got an answer. Delta hedging - is a first order of Tailor series. Neglect of other members creates error. Therefore hedge is not perfect.
lkjldfkjhljk's user avatar
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stdev of delta hedged portfolio for call option !=0. Why?

Disclaimer - I did not read your code. According to what I understand, your stdev is the stdev across 100,000 values of total debt at the maturity of those 100,000 simulations (where the underlying ...
KaiSqDist's user avatar
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1 vote

Is the Black Scholes PDE actually immediate from Ito's lemma?

The derivations of the Black & Scholes PDE being accurate or not has absolutely nothing to do with whether we write the Ito formula for the call price, in differential form, $$\tag1 dC=C_t\,dt+C_s\...
Kurt G.'s user avatar
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Black-Scholes formula proof, without stochastic integration

There are two holes in your proof Why value is given by expectation at all How to choose $\mu$ and $\sigma$ Girsanov tells you that $\sigma$ stays historical, 1) comes from fundamental pricing ...
achirikhin's user avatar
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Obtain B-S-M from a binomial tree as n goes to infinty using Lebesgue integral

By CLT, binomial distribution becomes normal as you increase steps $n$. $log(S(T))=log(S0)+klog(u)+(n-k)log(d)$ is thus a shifted normal distribution, and so $S(T)$ is lognormal.
Arshdeep's user avatar
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