Ezy
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5 answers
18 votes
3k views
Why does Kelly maximise $E[\log\space G]$ rather than simply $E[G]$?
Accepted answer
12 votes

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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1 answers
4 votes
5k views
Positive theta on a long put?
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7 votes

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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1 answers
3 votes
288 views
How to calculate the expectation of Poisson process when its intensity is also stochastic
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7 votes

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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3 answers
1 votes
252 views
Can you model the LIBOR rate as a geometric Brownian motion?
6 votes

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

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1 answers
3 votes
91 views
How to check if $ E [\exp \{ \int_0^t \frac{Y_u^2}{1+Y_u^2}du \}]< \infty $
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5 votes

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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4 answers
70 votes
43k views
What are the quantitative finance books that we should all have in our shelves?
5 votes

« 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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1 answers
1 votes
145 views
Why are implied volatility and the volatility required for an option to be profitable two different things?
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5 votes

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

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3 answers
3 votes
167 views
What's the logic behind 3-10 UST yield inversion predicting recession?
4 votes

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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1 answers
4 votes
1k views
Realized volatility forecast vs Implied volatility
4 votes

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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3 answers
3 votes
779 views
Calculating Sharpe Ratio with dynamic position sizing
4 votes

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 ...

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1 answers
1 votes
167 views
How to modify binomial tree to incorporate one more asset?
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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 ...

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2 answers
3 votes
121 views
Conditional Expectation with Indicator Functions for Poisson Process First Jump Time (Option Pricing PDE)
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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2 answers
4 votes
633 views
Application of Ito's lemma
3 votes

$t$ 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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2 answers
1 votes
508 views
why gamma decreases when option is deep in the money?
3 votes

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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2 answers
-2 votes
1k views
Least-Squares-Monte-Carlo by Neural Network Estimator for pricing American Option Python
3 votes

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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1 answers
4 votes
654 views
Splitting theta from vol carry
3 votes

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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1 answers
4 votes
539 views
Risk neutral valuation formula
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3 votes

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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4 answers
2 votes
177 views
How likely it is that a strategy profits are explained by luck?
3 votes

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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1 answers
3 votes
1k views
Why my implementation of CRR model does not converge?
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3 votes

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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2 answers
1 votes
1k views
How does a high frequency trading bot work?
2 votes

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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2 answers
3 votes
191 views
Are leveraged ETFs cheaper than using leverage?
2 votes

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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2 answers
2 votes
202 views
Failing Jarque-Bera test but residuals looks normal on q-q plot and histogram
2 votes

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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1 answers
0 votes
85 views
Why does a higher stock value imply a higher call option value
2 votes

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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1 answers
2 votes
64 views
Question about inverse leverage etfs
2 votes

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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4 answers
4 votes
558 views
Modelling HFT data
2 votes

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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1 answers
1 votes
181 views
Iron condor with positive vega
2 votes

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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1 answers
2 votes
449 views
Intuition behind one factor Merton model for probability of default?
2 votes

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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1 answers
2 votes
105 views
Getting rate from a share's given futures price, with known dividend information
2 votes

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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1 answers
2 votes
152 views
Markowitz portfolio risk with PV01 instead of variance
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2 votes

$\rho$ 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.

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1 answers
-2 votes
758 views
Work hours as a quantitative finance worker
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2 votes

Quants typically do not work a set number of hours per day. Although average hours are from like 8 am to say 6 pm, people are usually expected to be flexible depending on many factors such as: need to ...

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