Questions about models for the valuation of option contracts.

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The basic principle of the construction a portfolio of options

I have a question like this. Assume today's date is 9 January 2016 and XYZ's share price stands at $10. On 8 November 2016 there is a Presidential election and you believe that depending on who is ...
4
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5answers
522 views

Consensus on Cauchy distribution for stock prices

What is the general consensus for using a Cauchy distribution to model stock prices? I can't find much after researching online and wonder if it has been tried and discarded. My motivation is to find ...
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1answer
140 views

What is the stochastic differential of a general semimartingale?

By using the canonical representation of a semimartingale in Eberlein, Glau and Papapantoleon's "Analysis of Fourier Transform Valuation Formulas and Applications", on page 3: $$H = B + H^c + h(x) ...
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1answer
198 views

How to construct the binomial model for European option?

The annual interest rate is 5.3% and the annualized volatility of a non-dividend paying stock over the next six months will be 12.5% (annualized). i) Construct binomial trees of 5, 10 and 30 periods ...
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4answers
527 views

compute sharpe ratio for options?

Calculating sharpe ratio for shares is a straight forward task: (average returns - risk free ) / standard deviation. However i remain baffled as to how to tackle the task for options, can someone ...
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4answers
2k views

Risk Neutral Probability

I read that an option prices is the expected value of the payout under the risk neutral probability. Intuitively why is the expectation taken with respect to risk neutral as opposed to the actual ...
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4answers
699 views

From Fourier Transforms to Option Values

I am trying to understand how Fourier transforms & Characteristics functions can be used to calculate option values. However, I am having difficulty following the process that is used in several ...
4
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1answer
196 views

Can option prices be characterised by an ODE?

If a stock price, $S(t)$, is governed by a geometric brownian motion. Is it possible to characterise the value of an option $V(S,t)$ as an ODE rather than a PDE (given $S$ is itself a function of ...
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265 views

Pricing options and bid-ask spread

Consider a non-liquid option market with a wide bid-ask spreads across all strikes. Spot: \$52 A snapshot of the \$50 strike shows: ...
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2answers
299 views

Is there a contradiciton between option prices being martingales and the use of options for speculation?

It seems like there is a contradiction between the fact the option pricing is risk-neutral and the large amount of option trading that is done for speculation. Since the option is risk-neutral, a ...
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0answers
117 views

Do you use software for finite element valuation or do you roll your own?

Engineers put a lot of time and effort in developping high quality finite element (FE) software (deal.II, Dune, Elmer,...). So I was wondering if some of those tools would be suitable for quantitative ...
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1answer
169 views

reinsurance pricing equivalent to option pricing

Is it true that pricing a reinsurance contact is equivalent to pricing an option. Basically a reinsurance just cuts off the risk exposure of the insured institution to a threshold say $K$. So if we ...
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1answer
2k views

Seagull option strategy - clear example

It looks like the subject of seagull option strategy is not as clearly explained as for other strategies (butterly, bull,bear spread). Thus, can someone provide a clear example of what you buy and ...
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0answers
106 views

Basket option density in BS model

Let X and Y be two GBM’s, they have each a univariate log-normal distribution for some time t, that is $X_t\sim{LnN(µ_x, σ^2_x)}$, $Y_t\sim{LnN(µ_y, σ^2_y})$ and $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
3
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1answer
248 views

options pricing using vwap

This is a question about why options prices do not take volume into account. The popular option valuation formula "black-scholes" certainly does not account for this and I don't suggest that it does. ...
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0answers
90 views

Do some option pricing models allow for misspecification and what does it mean?

This is to some extent a theoretical question and maybe we can work together to produce some input and output. Diverse option pricing models are reported to be misspecified in various studies. One ...
4
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1answer
224 views

How does out-of-sample option pricing work in practice?

When estimating in-sample option prices, one usually estimates the structural parameters $\theta_t$ using all information up to time $t$, and then prices the option at time $t$ using the obtained ...
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1answer
130 views

Am I reading this correctly? probability way too small with BS model

For a stock trading at $27, $28 strike, 0% interest, 15% annual vol, and one day until expiration there is about a 1 in 17000 chance of it being exercised? $d_2 = ...
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1answer
112 views

Symmetry of option-implied probability density

I was wondering whether the option implied probability density of the log returns: $x = \ln\left(\frac{S}{S_0}\right)$ with S the value of a certain stock, is always symmetric ? I was asking myself ...
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2answers
285 views

how to calculate more efficient volatility figure than historical volatility?

can we use alpha value to calculate option price instead of historical volatility. And if we can please explain how. I am doing my MMS in Finance and this for a project i am doing. the project is ...
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0answers
353 views

Implied volatility and greeks for american option with discrete dividends

What methods are available to calculate IV and greeks for an american option with discrete dividends, and how do they compare? Should I use Roll-Geske-Whaley and solve for a given option price?
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2answers
3k views

How to numerically obtain delta?

The delta in option pricing, also called the hedge ratio, is expressed as the sensitivity of the option price to the underlying price change. The analytical solution for the most common option ...
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2answers
335 views

Black-Scholes fastest computation method

What is the fastest way to numerically compute Black-Scholes-Merton option prices? I'm trying to find fastest and still precise method. Currently I'm using numerical approximation of Normal cdf with ...
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0answers
157 views

How to statistically compare the pricing errors of various option pricing models?

I have three different option pricing models, for which I computed the in-sample and out-of-sample pricing errors. Now I want to test the pricing performance of these three option pricing models ...
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5answers
2k views

Why Drifts are not in the Black Scholes Formula

This question has puzzled me for a while. We all know geometric brownian motions have drifts $\mu$: $dS / S = \mu dt + \sigma dW$ and different stocks have different drifts of $\mu$. Why would ...
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4answers
2k views

How to calculate the implied volatility using the binomial options pricing model

I want to calculate IV for american options with dividends. So far I have found algorithms to calculate the option price given a volatility. Please can you point me to paper or implementation (R, ...
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2answers
502 views

Is the price of European put option monotone in volatility if we replace BM in Black-Scholes with a general Levy process?

Under the Black-Scholes model, we have the European put option is $\mathbb{E} [e^{-rt}(K-S_t)]$, where we take $\log(S_t)=X_t$ and $dX_t= \sigma dW_t - \dfrac{1}{2}\sigma^2 dt + rdt$. Here the option ...
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2answers
231 views

Change option B&S pricing

Consider a market composed by two stocks whose prices $X$ and $Y$ are given by B&S diffusion $$dX_t= \mu X_t dt+ \sigma X_tdW_t$$ $$dY_t= \mu Y_t dt+ \sigma Y_tdB_t$$ Supposing the market is ...
3
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1answer
136 views

Are there any good benchmarks for performance of vanilla option pricing code?

I've seen parsec (http://parsec.cs.princeton.edu/index.htm), which has a PDE pricing component, but the distribution is enormous and I haven't bothered to try to download it for review. I'm ...
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5answers
2k views

Call vs. Put Option

I have two interrelated questions that have been bothering me for some time. I have read all the stuff online and it still doesn't make sense to me: Let us assume: 0% interest rate (both hedge ...
5
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1answer
1k views

Longstaff-Schwartz (Least Squares Monte Carlo) applied to American Options

I'm working on an implementation in R of Longstaff & Schwartz method from the this 2001 article. I've managed to build code that replicates their prices in table 1 (p. 127), but only for the ones ...
3
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2answers
322 views

How do you know if if an option is priced correctly?

Besides obvious extreme examples (ie volatility going to infinity, infinite time, zero time, or zero volatility, deep OTM/ITM ) how does one gauge if an option is 'correct' or at least in the ...
3
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1answer
170 views

Foward-start option pricing

Consider a probability filtred space $(\Omega, \mathcal F, \mathbb F, \mathbb P)$, where $\mathbb F = (\mathcal F_t)_{0\leq t\leq T}$ satisfing the habitual conditions and is generated by $1 d $- ...
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1answer
199 views

Testing Black Scholes Analytical Options Pricer

I've written some code to calculate European option prices using the Black-Scholes analytical method. Can somebody recommend a good way to test that code? I have looked at option pricers online like ...
4
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2answers
625 views

Is drift rate the same as interest rate in risk-neutral random walk when using Monte Carlo for option pricing?

When using following risk-neutral random walk $$\delta S = rS \delta t + \sigma S \sqrt{\delta t} \phi$$ where $\phi \sim N(0,1)$. Now when a text mentions drift = 5% does that mean that interest ...
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1answer
235 views

Good Model Calibration Books/Papers for Common Option Pricing Models

I am trying to find a good book which focuses on the model calibration. I just want to know generally, what are the most common methods of model calibration(such as Black-Scholes Model, Stochastic ...
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1answer
1k views

Taylor series expansion (Volatility Trading book) explanation sought

I am currently reading Volatility Trading, I have only just started, but I am trying to understand a "derivation from first principles" of the BSM pricing model. I understand how the value of a long ...
0
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1answer
106 views

Reference on SDE driven by jump processes

Are there reference on SDE driven by jump proccesses? e.g. Shepard-Nielson Model
2
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1answer
131 views

American Option price formula assuming a logLaplace distribution?

What are $d_1$ and $d_2$ for Laplace? may be running before walking. When I tried to use the equations provided, the pricing became extremely lopsided, with the calls being routinely double puts. ...
6
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1answer
257 views

Upper bound concerning Snell envelope

Consider a non-negative continuous process $X = \left (X_t \right)_ {t\geq 0}$ satisfying $ \mathbb E \left \{ \bar X \right\}< \infty $ (where $ \bar X =\sup _{0\leq t \leq T} X_t $) and its ...
3
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1answer
271 views

Multiple Discrete Dividends

Using the recombining tree model as described in Haug's Option Pricing Forumla one can factor in multiple future discrete dividends when calculating the option value and greeks. What's unclear is ...
0
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1answer
168 views

Numerical difficulties in fitting option prices

In [1], the authors state that "Although some studies apply the curve-fitting method directly to option prices, the severely nonlinear relationship between option price and strike price often leads to ...
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2answers
864 views

How to calculate Vomma of Black Scholes model

This source (PDF) gives the closed-form for vomma (or volga, i.e. the second derivative of price w.r.t. volatility) of the Black Scholes option pricing model as: ...
3
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1answer
353 views

Choice of epsilon for numerical calculation of vega in binomial option pricing model

I have a binomial option-pricing model (I don't think the details of how its implemented are relevant). However, when I go to calculate vega, I am essentially running the model a second time with new ...
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2answers
2k views

How do we use option price models (like Black-Scholes Model) to make money in practice?

In quantitative finance, we know we have a lot of option price models such as geometric Brownian motion model (Black-Scholes models), stochastic volatility model (Heston), jump diffusion models and so ...
0
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1answer
543 views

Which prediction market model is efficient and simple to use?

For a college project I'm tasked with implementing prediction market. Which model of it I'd better choose? I want something useful and simple enough for other people to quickly understand and use. ...
2
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1answer
863 views

what is the implied volatility on a basket of options

If I have 4 optionable stocks A,B,C,D and each different implied volatilies,IV-A,IV-B,IV-C,IV-D. How do get the implied volatility for a basket option on A,B,C,D where the basket weights are w-A=.6, ...
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2answers
2k views

price of a “Cash-or-nothing binary call option”

I'm stuck with one homework problem here: Assume there is a geometric Brownian motion \begin{equation} dS_t=\mu S_t dt + \sigma S_t dW_t \end{equation} Assume the stock pays dividend, with the ...
6
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3answers
352 views

Replicating portfolio and risk-neutral pricing for interest rate options

For equity options, the pricing of options depends on the existence of a replicating portfolio, so you can price the option as the constituents of that replicating portfolio. However, I am not seeing ...
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2answers
1k views

Basket option pricing: step by step tutorial for beginners

I would like to learn how to price options written on basket of several underlyings. I've never tried to do it and I would appreciate if you can provide some documents, papers, web sites and so on in ...