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30

In general there are two basic ways to make money out of your option pricing models: Sell side (market maker, risk neutral): You use these models to calculate your greeks to hedge your portfolio, so that you live on the spread. Buy side (market/risk taker): You use your model to find mispriced options in the market and buy/sell accordingly. (A third ...


26

It's an interesting question. I particularly agree with the $\mathbb{Q}-\mathbb{P}$ dichotomy mentioned by many. I would add to the other answers that, come to think of it, the Black-Scholes postulated Geometric Brownian Motion could be interpreted as an AR(1) process on the logarithm of the stock price as you discretise the SDE from which it is a solution,...


15

Agree with all of vonjd's points though I like to add the following: First of all, market practitioners do not read options prices or set options prices in the market, they price the option through models primarily on the basis of implied volatility. Im plied volatility is actually traded, options prices is what comes out on the other side. I know there was ...


14

I think you need to differentiate between Q-quants vs P-quants. The former might not use Econometrics, but P-quants use them a lot.


11

Traditional econometric (time series) models are of little or no value in forecasting market prices for purposes of "making money", i.e, generating excess return over a benchmark in an asset management setting. They have some limited value in strategic and tactical asset allocation. The ineffectiveness of time-series modeling in asset management stems ...


9

This the "Joint Hypothesis Problem". Basically, any test for abnormal returns is also implicitly a test of the model you use to define "abnormal". If you see a significant and positive $\alpha$, that could either mean that you actually are generating excess risk-adjusted returns, or it could mean that your risk model is incomplete. This is basically what ...


9

The best answer to your question is probably given by the Nobel prize committee itself in "The Prize in Economic Sciences 2003 - Advanced Information" document. You should read it in full. Below is an excerpt. According to the committee: Financial economists have long since known that volatility in returns tends to cluster and that the marginal ...


8

The original Nelson Siegel paper describes a parsimonious model of the term structure using only four or three (if $\lambda_t$ is fixed). Filipovic (1999) proves that this model can never be used in a arbitrage free context, paraphrasing the abstract: We introduce the class of consistent state space processes, which have the property to provide an ...


7

The primary alternative to Bayesian subjective probabilities is the frequentist approach. This would involve measuring the % of times where international bonds outperformed US bonds by 25 bps over the relevant period in market history and using that as your confidence level. A quantitative view in-between the Bayesian and frequentist approaches would be a ...


7

Multi-fractal models can be applied to the modeling and forecasting of volatility. I read the following book with much interest and actually setup couple models in order to compare performance vs Garch family models and the application of multi-fractals much better captures discontinuous regime-changes than traditional volatility models. Multifractal-...


7

Behavioral Finance is a wide topic, which I believe is still today underestimated by many financial professionals. How can it be used by quants? Well, in portfolio optimization it can be used "as an overlay" in the form of constraints where the optimal portfolio can not be too different from the current portfolio, because clients have behavioral biases ...


7

Having thought about this I think the following reason is also important and wasn't mentioned so far: When you look at the inner working of this whole class of econometric models it all boils down to the following: It is possible (under some reasonable assumptions) to express any $MA(q)$ model as an $AR(\infty)$ model (and vice-versa for expressing $AR(p)$ ...


6

SMM stands for single-month mortality and CPR stands for constant (or conditional) prepayment rate. They're both units of voluntary prepayment rates ($CPR = 1-(1-SMM)^{12}$). They could be based on either estimated or actual prepayments. Where to get actual MBS prepayment data will depend on what type(s) of MBS pools you're modeling (e.g. agency, ...


6

I would say Start with Black Scholes to look at accuracy. In particular, you have a closed formula and you know what the characteristic function for lognormal is. Running FFT and comparing FFT pricing with the closed formula will give you an idea of what are the convergence issues, what is the behaviour at the boundaries (extreme strikes) etcetera. Then ...


6

The model of choice depends on the purpose of the exercise. In general there are two types of models: Equilibrium models: These are general used use for "fitting" the spot curve to the discount function available in the market. So different models will give you different yield curves. One can use this information to see the relative value of implementing a ...


6

I think you are having it backwards: Optimising your lookback period is a sure recipe for disaster because it introduces data snooping bias. To develop a robust trading strategy you have to check whether it is sufficiently stable with different lookback periods (e.g. in a certain range). If results differ significantly that is a good sign that your system ...


6

My answer is very much in the spirit of Kiwiakos' answer. E.g. in this paper (where I am one of the coauthors) we use VMA (vector moving average) models (in the multivariate case) and AR models in the univariate case to calculate proper scaling of volatility or its contributions if there are (cross-) auto-correlations. This happens in the P world due to ...


6

In the context of option pricing, "implied volatility" always refers to the equivalent diffusion coefficient in the geometric Brownian motion (GBM) dynamics that is necessary to match an observed European plain vanilla price for a given strike and maturity. When talking about "model implied volatility smile", what is meant is that: You choose some pricing ...


5

Couple points I like to make: There exists no reliable model that can even predict future price returns (risk premiums, excess returns, whatever you want to call it) beyond a year, run as fast as you can if you hear from someone who claims he can predict risk premiums 10 years out, whether reliably or not. It makes zero sense and clearly comes from either a ...


5

The answers above are good, but I suspect they will be unsatisfactory if you are looking for implementations that are successful in practice. The sort of bottom-up analysis championed by Soros is very difficult to carry out in a rigorous, quantitative manner. This is true very generally, not just in finance. There are certainly models of financial markets ...


5

The most important questions in my opinion (besides all the mathematical questions and robustness tests that have to be performed anyway) are: Why is this model working in the first place? What is the economic rationale behind it? Why have the returns not been arbitraged away? Who is paying for your returns and why? Is this situation likely to be ...


5

You don't mention if the puts in question are exotic or vanilla, but assuming they are vanilla, you should read this paper by Chen and Joshi. In it, they find optimal performance by using smoothed, truncated Tian-parameter binomial lattices with Richardson extrapolation -- where the idea is to run one extra low-cost (long $\Delta T$) tree in order to ...


5

Yes, a Monte Carlo simulation (MC) is what you need. It is a well known and documented approach with many uses in finance, science and engineering. MC simulations are used to simulate the returns of complex financial assets or in your case returns of business ventures under uncertainty. Your input variables ($x_1, x_2,\cdots, x_n$) are uncertain. If you ...


5

I understand that Moody's uses an empirical distribution while KMV uses a normal distribution in order to calculate these probabilities KMV doesn't use a normal distribution to map distance to default to a probability of default (EDF in the KMV model). It uses a proprietary database. By a strict structural interpretation, $EDF$, the expected default ...


5

We first list the assumptions. \begin{align*} g_{t+1} &= \mu_g + \sigma_{g, t} z_{g, t+1}, \tag{1}\\ \sigma_{g, t+1}^2 &= a_{\sigma} + \rho_{\sigma} \sigma_{g, t}^2 + \sqrt{q_t} z_{\sigma, t+1}, \tag{2} \\ q_{t+1} &= a_{q} + \rho_q q_t + \varphi_q \sqrt{q_t} z_{q, t+1}. \tag{3} \end{align*} Moreover, \begin{align*} r_{t+1} &= -\ln \delta +\...


5

one of the most fundamental results states that the binomial model converges towards the Black Scholes model if the step size $\Delta t$ converges to zero. The Black Scholes model is an option pricing model where the underlying is given by $$ S_T = S_0 \cdot \exp \Bigl(\sigma W_T - \frac 12 \sigma^2 T \Bigr). $$ By choosing $$ u = \exp(\sigma \sqrt{\...


4

In practice all impact models are sub-linear. Despite this is fact (seen in many academic publications, commercial and proprietary models), there is an interesting argument for using a linear impact models (other than being careful and pessimistic). Would anyone try to build a model, this approach would be also more parsimonious with less parameters to fit. ...


4

Question “When we speak about Parrondo's Paradox in relation to stock markets, is there a direct relation between both of them?” Professor Parrondo: I could say, no, no direct with the original ones, because the probability in the original ones depends from how much capital do you have, then it is a random walk with no uniform probabilities and it is ...


4

I haven't posted on SE much, so hope you will not mind if I also answer some comments here. The best paper I have seen articulating what Soros does is by Flavia Cymbalista, a psychologist writing in the tradition of Eugen Gendlin. It's a very brainy paper, and Soros himself has spoken favourably about it. A link to it is here: http://www.martinkronicle....


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