Kiwiakos
  • Member for 7 years, 6 months
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How can an inverted yield curve in a liquid market exist?
4 votes

Inverted curves (typically) appear when the economy is overheating. There is full employment but investment demand is still there and it is creating inflationary pressures. The central bank increases ...

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What is the effect of dividend yield being greater than the risk-free rate to American options pricing?
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4 votes

I think that for any $q>0$ it becomes optimal to exercise an American call for a sufficiently high spot price $S$: if the spot increases enough, the dividend yield corresponds to sufficient cash ...

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Portfolio Theory: Why is so much effort put into the reduction of estimation errors?
3 votes

In MPT investors maximize ex ante expected return for a given level of ex ante variance. Gaussian-ity or iid-ness of returns are not requirements. The problem is estimating these ex-ante quantities ...

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Black Scholes biases
3 votes

Perhaps they mean that if you use the ATM implied volatity as an input to price ITM and OTM options, then some will be underpriced and some overpriced compared to the true price observed in the market....

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Find the parameter $d$ of the Affine Option Pricing Model in Duffie, Pan and Singleton (2000)
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3 votes

$d$ is a vector that collapses the $n$-dimensional vector into a real number. In the BS case $d=1$. There is nothing to be estimated. Also not that in practice affine pricing is done through FFT (and ...

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Is there a way to meaningfully generate daily returns from monthly?
3 votes

Kalman filter (or similar methods) are quite well suited to deal with observations that are of different sampling frequencies and/or asynchronous.

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existence of implied volatility
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3 votes

You can show that "the implied variance of an ATM short maturity option is equal to the expectation under the risk neutral measure of the integrated variance over the life of the option." As you move ...

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Calibration of Heston model
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3 votes

If you want to calibrate on time series, then you have a 'non linear filtering' problem, since volatility is latent. There have been papers from late 90s/ early 00s that do that: Google for Heston ...

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Sensitivity of short-term vs long term options' IV
3 votes

Yes. Implied vol is (very loosely speaking) the risk neutral expectation of the realized volatility over the life of the option. A 10Y implied vol is an average over 10 years, and therefore is ...

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Is there a python code for estimating the parameters of geometric brownian motion?
3 votes

The code below pulls AAPL time series from Yahoo Finance, computes mean/std and simulates 100 paths that are 20 days long. Input: import pandas as pd import numpy as np from numpy.random import ...

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What can I use to measure of diversification?
3 votes

I use the 'implied correlation' defined as $$ \rho = \frac{V^2_P-\sum V^2_j}{(\sum V_j)^2-\sum V^2_j} $$ for $V_p$ the VaR (or volatility) of the portfolio, and $V_j$ the VaRs (or volatilities) of the ...

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Relationship between risk-neutral probability and subjective probability
3 votes

Standard Finance/Utility theory dictates that all future cash-flows are priced via the marginal rate of substitution. For example, say that $X_T$ is the random variable that represents this cash-flow ...

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What methods are there for showing a time series is mean reverting?
3 votes

In econometrics all these tests are under the banner of 'Unit Root Tests'. There is a vast body of literature that deals with their formulation, treatment and pifalls.

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How is the default probability implied from market implied CDS spreads for CVA/DVA calculation?
3 votes

A methodology for estimating rating/ region/ sector proxies for ACVA calculations can be found here: http://www.nomura.com/resources/europe/pdfs/cva-cross-section.pdf Please let me know if you need ...

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On the interface between Quant finance and actuarial-science/insurance-math
3 votes

The classical connection is the http://en.m.wikipedia.org/wiki/Esscher_transform developed for actuaries in 1932 which essentially transforms the objective probability measure into the risk neutral ...

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Local volatility surface corresponding to the implied volatility surface
3 votes

Loosely speaking: Local volatility is the instantaneous volatility after time T if the spot is S at that time. Implied volatility is the expected integrated volatility from today up to time T if the ...

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How to estimate parameters of geometric brownian motion with time-varying mean?
3 votes

I would say Take log of first equation to get rid of dependence on $x_t$ Apply Kalman filter equations to estimate parameters I believe Conrad and Kaul (1988) J of Business do exactly what you ...

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Brownian Bridge's first passage time distribution
Accepted answer
3 votes

What about this sketch of an answer: Let's put $T=1$ in your formula to simplify the notation. Then $Y_b(t)$ is a Brownian bridge where $Y_b(0)=0$ and $Y_b(1)=b$. This can be written as $Y_b(t) = b\ ...

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Why is Yahoo finance's historical prices so high
2 votes

Prices (and potentially volumes) have been adjusted for historical corporate actions. For example, if there was a 10:1 split in the past, then todays share is equivalent to 1/10th of a share before ...

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Why " Even if the underlying asset price remains unchanged, the option delta for an in-the-money option increases as expiration nears"
2 votes

If the call is ITM, ie $K<S$, as expiry approaches the likelihood that the option will be exercised increases, as there is now less time for it to go OTM. Delta is the position that the hedger is ...

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Convergence of the distribution of 0.05 quantiles through Monte-Carlo simulation
2 votes

Two comments: Normal returns should always be in $[-1,+\infty)$. I believe that the way you sample $R_i$ from Stable directly violates that. You might want to sample $\log (1+R_i)$ from Stable ...

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Stochastic volatility
2 votes

The answer is yes. In fact, there always exist a 'Black Scholes like' formula. Easy to show too. If the risk neutral distribution of the price has cumulative density $P$ and probability density $p$, ...

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Stochastic Simulation vs percentile-to-percentile map
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2 votes

What you describe is a very simple quasi monte carlo, where the 'random' points are equally spaced in probability space. Like numerical integration. Sometimes you can use it, but in general you will ...

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The use of $p$-value in finance after the recent statement of ASA (American Statistical Association)
2 votes

Deidre McCloskey has been going on about this for as long as I can remember. See for example the aptly titled : "The cult of statistical significance: How the standard error costs us jobs, justice and ...

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Bounded Stochastic discrete process
2 votes

I believe that the process you postulate has a Beta conditional distribution. If my memory serves me well, I have encountered it in the book by Liptser and Shiryayev "Statistics of Random Processes" ...

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Where to find pricing formulas for affine stochastic volatility jump-diffusion models?
2 votes

Do these work for you? P34 of http://web.mit.edu/junpan/www/SVJ.pdf P1360 of http://www.darrellduffie.com/uploads/pubs/DuffiePanSingleton2000.pdf P2045 of http://www.math.ku.dk/~rolf/bakshi.pdf

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Value of a continuous cash flow until a random time
2 votes

Pricing always takes place under the risk neutral probability measure. In fact, this would make the price more conservative (i.e. lower) with respect to risk; if you priced it under the true measure ...

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Is it too important that my residuals be normal? I am Using an ARMA/GARCH model
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2 votes

To get it out the way: you cannot ask 'what model is better' without a reference to what its use is. Do you want to test for the mean or the AR parameter to trade it? Do you want to calculate VaR? Do ...

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does there need to be risk-neutral agents in the market to enforce risk-neutral pricing?
2 votes

No. Actually "risk neutral pricing" does not make assumptions on the risk preferences of the agents. Securities are priced as if agents were risk neutral (that is to say as a straight expectation of ...

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Martingale Measure for Vasicek process
2 votes

I think that you are a bit confused: the support of the Black-Scholes model is $(0,+\infty)$, that is to say the underlying asset price is non-negative, like a stock. The Vasicek model has an OU ...

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