Questions about models for the valuation of option contracts.

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1answer
691 views

How to explain the path dependency in binomial tree model to price options?

I'm new to quantitative finance, so I'm confused with the so-called path dependency in binomial tree model. Originally I thought the path dependency exists because in binomial tree model, we will ...
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4answers
1k 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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0answers
442 views

R or Matlab code for Multi-Barrier-Options (3 or more underlyings)

I am looking for R or Matlab code examples of multi-barrier-options (or multi-barrier reverse convertibles) with at least 3 underlyings. Do you have such code or can you point me to a place where I ...
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0answers
120 views

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 ...
0
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1answer
242 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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3answers
2k views

When do Finite Element method provide considerable advantage over Finite Differences for option pricing?

I'm looking for concrete examples where a Finite Element method (FEM) provides a considerable advantages (e.g. in convergence rate, accuracy, stability, etc.) over the Finite Difference method (FDM) ...
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1answer
257 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 $t$)?...
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4answers
4k views

True or False? An option's price will always be greater than or equal to its intrinsic value

Since if the option's price is lower than its intrinsic value (eg. strike price - current stock price for puts), then an arbitrage opportunity arises from buying the option at bargain and then ...
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0answers
357 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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0answers
129 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
203 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
5k 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
137 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 $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
4
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1answer
249 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 ...
9
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2answers
771 views

Extensions of Black-Scholes model

For the Black-Scholes model my feeling is that the volatility parameter is like sweeping stuff under the rug. Are there models which improve on the volatility aspect of Black-Scholes by adding other ...
3
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1answer
475 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
106 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 ...
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1answer
1k views

Can anyone give me a practical example of pricing and calculating IV on equity index options? (i.e. using real market data)

I have been trading (mostly equity and equity index) options for a while now and I want to apply a slightly more quantitative approach to my trading - specifically, by calculating IV and incorporating ...
0
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1answer
128 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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1answer
136 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 = \frac{1}{.15\sqrt{1/252}}\left[\ln\...
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2answers
371 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
626 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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4answers
4k 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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0answers
250 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 ...
3
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2answers
3k 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 ...
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1answer
2k 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 ...
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2answers
2k 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: $$S_{0}e^{-qT}\sqrt{T}\frac{1}{\sqrt{...
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1answer
201 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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2answers
521 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 ...
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10answers
2k views

Using Black-Scholes equations to “buy” stocks

From what I understand, Black-Scholes equation in finance is used to price options which are a contract between a potential buyer and a seller. Can I use this mathematical framework to "buy" a stock? ...
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1answer
244 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 ...
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1answer
571 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
1k 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
369 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 ...
5
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1answer
3k 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 ...
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1answer
114 views

Reference on SDE driven by jump processes

Are there reference on SDE driven by jump proccesses? e.g. Shepard-Nielson Model
6
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1answer
277 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 ...
2
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1answer
142 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. ...
3
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1answer
718 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 ...
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1answer
204 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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1answer
862 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. (...
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2answers
3k 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 ...
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4answers
2k views

Methods for pricing options

I'm looking at doing some research drawing comparisons between various methods of approaching option pricing. I'm aware of the Monte Carlo simulation for option pricing, Black-Scholes, and that ...
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3answers
2k views

Longstaff Schwartz method

I try to implemente the LSM method with this algorithm but my price is always too low. By example for an American put option with the following parameters: S0 = 36, Strike = 40, rate = 6%, T = 1 ...
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1answer
2k 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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0answers
286 views

Pricing a Power Contract derivative security

I'm trying to price a "power contract" and would appreciate guidance on the next step. The payoff at time $T$ is $(S(T)/K)^\alpha$, where $K > 0$, $\alpha \in \mathbb{N}$, $T > 0$. $S$ is ...
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0answers
193 views

Probability Density of Returns of Bonus Certificates

Could anyone please help me with the following? I need to generate a histogram (resp. probability density) of returns of a bonus-certificate. A bonus-certificate can be replicated by an underlying ...
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697 views

How to show that this weak scheme is a cubature scheme?

Weak schemes, such as Ninomiya-Victoir or Ninomiya-Ninomiya, are typically used for discretization of stochastic volatility models such as the Heston Model. Can anyone familiar with Cubature on ...
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1answer
495 views

Question on OptionMetrics: “Strike Price times 1000” differs too much from Index price

I have a question regarding the strike price that is given on OptionMetrics. My goal is to primarily retrieve options prices of a specific maturity with strike prices that are 20% in-the-money, at-the-...
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1answer
511 views

Interpreting QuantLlib implied volatility numbers

I am using QuantLib to calculate implied volatilities. I am trying to understand the calculated figures (especially, when compared to historical volatility). The calculated implied volatility numbers ...