# Tag Info

22

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 ...

21

In the Interest Rates field there is one paradox in nowadays market conditions (i.e. since the crisis) that is quite tricky to properly understand. This is the fact that one need several curves to have a correct pricing of simple interest derivatives such as Swap with floating index set to some Libor reference. Simply and crudely speaking, you have to ...

18

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

There is a family of models that is so commonly used among practitioners that it can be almost regarded as standard. For a survey, check out Rob Almgren's entry in the Encyclopedia of Quantitative Finance. Check out also Barra, Axioma and Northfield's handbooks. In general, the impact term per unit traded currency is of the form MI \propto \sigma_n \cdot \...

13

You can forecast stock prices thru time-series models, cross-sectional, or panel models. There is considerable variation within these categories. In time-series models you would use an auto-regressive model such as an AR(1) where the independent variable is the dependent variable lagged by one period. Naturally, an AR(2) would consist of 2 lags and so on. ...

11

There is also the so-called Hakansson’s paradox that can be found in Derman's article on dynamic replication. Hakansson’s so-called paradox (Hakansson 1979, Merton 1992) encapsulates the skepticism about dynamic replication: if options can only be priced because they can be replicated, then, since they can be replicated, why are they needed at ...

11

A very good book addressing such "puzzles of finance" — highly recommended! Puzzles of Finance: Six Practical Problems and Their Remarkable Solutions by Mark P. Kritzman The paradoxes that are treated here are: Siegel's Paradox. Likelihood of Loss. Time Diversification. Why the Expected Return Is Not To Be Expected. Half Stocks All the Time or All ...

11

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.

10

I don't believe that there is a "standard" model (per say); in fact, there are many considerations around market impact models, so you would need to be more specific. At the most basic level, you might define market as $P_{first fill} - P_{last fill}$ once your order in actually in the order book (e.g. not including other costs like "opportunity cost"). ...

9

I don't think that there is a precise point in time when we can say that model is valid (well, it's a model not a law). For example, E. Derman in his article on Model risk describes the verification of model as a iterative process: It is impossible to avoid errors during model development, especially when they are created under trading floor duress .... ...

8

Keynes introduced this idea in the notion of a Keynesian Beauty contest: http://en.wikipedia.org/wiki/Keynesian_beauty_contest Anyone who uses a rolling window regression where the parameters and/or parameter estimates are re-fitted periodically are implicitly accounting for this reflexivity (i.e. the market's changing behavior as agents respond and adapt ...

8

Parrondo's paradox is a paradox in game theory that describes a losing strategy that wins in the long term. It seems the paradox is only used in textbook examples of finance and has little applications in practice, though.

8

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 ...

8

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 ...

7

Market makers covers a broad range of shops, from large investment banks to small proprietary trading firms. So working capital can be in the millions or the billions, and leverage can be anywhere from 2x to 30x. This is no different from buy-side firms, which includes a variety of both asset managers and retail investors. There is tons of diversity among ...

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

The paper "High Frequency Trading and The New-Market Makers" by Menkveld will likely have information that will be interesting to you. The paper breaks down the activity of one HFT in a European market. It provides statistics such as the # of trades, capital required, average profit, loss, etc. You can judge for yourself whether you trust the numbers based ...

6

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 ...

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

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-...

6

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 ...

6

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 +\...

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 ...

5

Not really a paradox, but kind of surprising that delta is not necessarily the derivative of option value with respect to the price of the underlying in the standard MBA one period binomial model. Suppose the realized return over the period is $R$, the stock price at the beginning is $s$ and can go to either $sd$ or $su$ at the end. We can replicate any ...

5

Since both $ER$ and $S$ are gaussian random, why not just assume their dependence is captured by their covariance, and make your draws from the bivariate normal distribution? It is hard to construct any other way of making two marginal gaussians cointegrated. Even if the variables were not gaussian, you would probably find yourself relating them using a ...

5

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 ...

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 ...

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

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 ...

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