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Maximizing $E[\log(G)]$ which corresponds to a concave utility function is a subtle way of incorporating risk aversion in the utility. Maximizing $E[G]$ is basically saying that you have linear ...

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If a european option value becomes lower than intrinsic value it gets negative time value. In this circumstance the theta becomes positive because as time approaches to expiry the option value has to ...

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You can condition on the value of $\lambda_t$. So $E[dN_t] = E[E[dN_t|\lambda_t]] = E[\lambda_t dt] = E[\lambda_t] dt$

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It is not reasonable because rates display a stationarity but brownian motion is not stationary. The variance of libor at a future time $t&gt;0$ conditional on the value at time $t=0$ does not scale ...

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If you make the change of variable $Y_t = \sinh U_t$ and apply Ito then you immediately get $$dU_t = 2dW_t$$ so the solution of your SDE is $$Y_t = \sinh\left(2W_t + C\right)$$ with $C$ a constant. ...

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« Stochastic differential equations » by Oksendal is my best reference on SDE for practionners who want a rigorous statement of all important results in the topic while maintaining a decent size for ...

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The implied volatility value 15.6% is an annualized number, not a weekly one.

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When the market enters a risk-off period the investors proceed to a rotation between more risk assets (commodities, equities etc...) to the less risky ones. At this point there is just a lot of supply/...

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On average the implied volatility is higher than realized volatility because you can easily imagine that dealers will ask customers to pay a premium to write them options and risk manage them you can ...

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To calculate the sharpe ratio of a strategy backtest you should ultimately go back in $space and calculate for every day your PNL (profit and loss), not returns, because at the end of the day this ... View answer 1 answers 1 votes 167 views Accepted answer 3 votes Under Black-Scholes assumption for the 2 assets$S_1$and$S_2$with volatilities$\sigma_{1,2}$and correlation$\rho$the value of this option has an explicit expression which is the Margrabe ... View answer 2 answers 3 votes 121 views 3 votes The density of the random variable$\tau$is like you pointed out; $$\phi(s):=E[\delta(\tau-s)|\tau \geq t] = e^{-\int_t^s\beta(u)du}\beta(s)$$ where we called$\delta$the Dirac density function ($...

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$t$ is fixed to simply apply Ito Lemma to $h(s,X_s)$ with the function $h: (s,x)\rightarrow f(t-s,x)$ and you get your answer. There's nothing special about it, I think you are a bit confused by the ...

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Gamma is not linked to the supply/demand for an option. It is a purely analytic effect that reflects the convexity of the product.

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In the non nn case your code does not implement the longstaff-schwartz algorithm so i am not sure what makes why you think it does. Longstaff-Schwartz is a Monte-Carlo method and you seem to be ...

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Well it all depends how theta is calculated in the first place. Depending on your pricing scheme those could be very different things. Anyways assuming that you are dealing with european vanilla then ...

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The absolute reference for starters which does not dwelve too much into mathematical details but enough to be accurate is Hull so i suggest you have a look at this book first. Options, Futures, and ...

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I believe that by "luck" you mean that you want to check if you can attribute the pnl of your strategy to something else than the "alpha" that it's trying to capture. The standard way of doing this ...

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from the look of it your discounting is incorrect because as you increase M you should discount with 1/(1+r0*t) (assuming r0=0.0214 is the annual interest rate where as you seem to discount by 1/(1+r0*...

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No. If you sent 10 orders for 1 btc and they all hit the matching engine then in any sane microstructure you should get your orders processed before the counter has time to process your 9 trailing ...

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Leveraged ETF have negative gamma: the higher the volatility of the underlying index the bigger the negative drag. This is a big pitfall of those instruments because one can be correct with the ...

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Your question is very general and it's hard to answer specifically without more details from you what are you trying to use this data for ? How big is your dataset ? Are you interested in the tails ...

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Instead of talking about an option you should apply your reasoning to the simpler example of the forward contract to see the flaw in your argument. Suppose the spot is a martingale process and ...

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You got it wrong the math says the opposite. According to the equations in the drift of the LETF is negatively impacted by the realized volatility which you completely skipped over. The realized ...

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Trades are obviously very important. At the elementary level, a market exists for the purpose of matching buyers and sellers and the mechanism adopted to establish price discovery in LOB is to have ...

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Just to be clear: please provide the 2 dates you are pricing your package at and the values of the spot and IV on each of those pricings. Also you are pricing very short dated options immediately ...

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Like you said the goal of this equation is to describe a simple model where the individual “well being” has correlation $\sqrt{p}$ with some systematic factor and receive also contribution from ...

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You do root search for such an equation. It works perfectly well assuming a solution exists given your parameters. Aside from this it is not clear to me why you would want to imply the interest rate ...

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$\rho$ needs to be the correlation matrix of bond yields and you also need to scale by the bond yield variances. All the dv01 scaling does is change the risk variables from price to yield.