Kiwiakos
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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 ...

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 ...

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 ...

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....

$d$ 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 ...

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

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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.

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 ...

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 ...

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 ...

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 ...
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 $Y_b(t) = b\ ... View answer 2 votes Prices (and potentially volumes) have been adjusted for historical corporate actions. For example, if there was a 10:1 split in the past, then todays share is equivalent to 1/10th of a share before ... View answer 2 votes If the call is ITM, ie$K<S$, as expiry approaches the likelihood that the option will be exercised increases, as there is now less time for it to go OTM. Delta is the position that the hedger is ... View answer 2 votes Two comments: Normal returns should always be in$[-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)$from Stable ... View answer 2 votes The answer is yes. In fact, there always exist a 'Black Scholes like' formula. Easy to show too. If the risk neutral distribution of the price has cumulative density$P$and probability density$p$, ... View answer Accepted answer 2 votes What you describe is a very simple quasi monte carlo, where the 'random' points are equally spaced in probability space. Like numerical integration. Sometimes you can use it, but in general you will ... View answer 2 votes Deidre McCloskey has been going on about this for as long as I can remember. See for example the aptly titled : "The cult of statistical significance: How the standard error costs us jobs, justice and ... View answer 2 votes I believe that the process you postulate has a Beta conditional distribution. If my memory serves me well, I have encountered it in the book by Liptser and Shiryayev "Statistics of Random Processes" ... View answer 2 votes Do these work for you? P34 of http://web.mit.edu/junpan/www/SVJ.pdf P1360 of http://www.darrellduffie.com/uploads/pubs/DuffiePanSingleton2000.pdf P2045 of http://www.math.ku.dk/~rolf/bakshi.pdf View answer 2 votes Pricing always takes place under the risk neutral probability measure. In fact, this would make the price more conservative (i.e. lower) with respect to risk; if you priced it under the true measure ... View answer Accepted answer 2 votes To get it out the way: you cannot ask 'what model is better' without a reference to what its use is. Do you want to test for the mean or the AR parameter to trade it? Do you want to calculate VaR? Do ... View answer 2 votes No. Actually "risk neutral pricing" does not make assumptions on the risk preferences of the agents. Securities are priced as if agents were risk neutral (that is to say as a straight expectation of ... View answer 2 votes I think that you are a bit confused: the support of the Black-Scholes model is$(0,+\infty)\$, that is to say the underlying asset price is non-negative, like a stock. The Vasicek model has an OU ...