Questions about models for the valuation of option contracts.

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EMM in incomplete markets

The simply put question is as follows: do we need to restrict ourselves to EMM exclusively when pricing European contingent claims (=option payoffs) even if markets are incomplete? In particular, a ...
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1answer
86 views

Simple pricing example confusion

This it taken from "Heard on the Street", Section B. Consider a market with $0$ risk-free rate, no transactions costs etc. The IBM stock costs \$75 and does not pay dividends. Design a security ...
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1answer
144 views

How to price this option without using BS framework

We have a stock at price 1 dollar which pays no dividend. Also we assume zero interest rate. When the price hits $H$ dollars for the first time where $H>1$, we can exercise the option and receive 1 ...
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2answers
77 views

Efficient numerical approaches for pricing American Options with multiple sources of noise

I am looking for efficient numerical approaches for pricing American options when two or more sources of noise are involved (the simplest case coming to mind would be the Heston Model) Eventhough I ...
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48 views

Incorporating a stochastic correlation structure into a multi-factor model

I am considering extending a multi-factor fixed income stochastic model (e.g. LIBOR-Market) to use stochastic correlation matrices instead of determinstic ones. For pricing instruments with short ...
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2answers
148 views

Options with a stochastic strike

Do options where the strike itself is a stochastic process exist? If they do - what are the motivations for such a product and where is it used ? Example: Call-Option with stochastic strike: ...
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3answers
251 views

How to choose a risk-neutral measure when the market is incomplete?

I am more of a probabilist than a financial mathematician. I am currently working on the features of American put options under a particular stochastic volatility model. Like most stochastic ...
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1answer
116 views

Does risk-neutral measure have anything to deal with risk-neutrality in utility theory?

Or simply: why do we call equivalent martingale measures as risk-neutral measures? In the utility or game theory, when we consider a person's preferences to certain outcomes, we often deal with the ...
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1answer
114 views

Effects of random-generator-choice on derivative's price

There is a plethora of pseudo-random-generators out there. Some of them are definetly better and some of them severily underperform. My standard tool is Mersenne Twister - when I need to generate ...
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2answers
294 views

Calculate volatility from call option price

Given call option price, what is the simplest formula to get the volatility value ? Test Data: ...
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1answer
261 views

Places to make quant code/tools publicly avaliable

Over the years I have developed several tools - including pricing, optimization and calibration tools - most in VBA, C# and C++ I would like to make them publicly avaliable. Aside from putting up my ...
2
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1answer
187 views

Call option on a Mutual Fund

I am trying to price a call option on a mutual fund. Given the lack of market implied data, I am going to estimate the fund´s expected volatility using as a reference its historical volatility ...
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178 views

Algorithmic Trading Model Calculation and Stale Data

I'd like ask everyone a more concurrency programming but definitely quant-finance related question. How do you deal with staleness of data in market hours as quote ticks are streaming and your model ...
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1answer
138 views

Implied probability density (Question 2 - Applications and Interpretation)

Using the second derivative of the Call-Option-Price one can try to recover the pricing density. Formally: Assuming a constant interst rate $r$ and also not making any assumptions on the model ...
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1answer
281 views

Is Behavioral Finance relevant to quants?

This topic has been prompted by the following question: Measuring Behavioral Finance Effects in Fund/Portfolio Manager Analysis After reading it and the comments below I started thinking whether ...
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1answer
175 views

Implied state price density (Question 1 - derivation of the formula)

I came upon the term "implied state price density" in a couple of papers. As far as I understand the concept one basically tries to extract the "pricing density" from the market data. For the sake ...
2
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0answers
112 views

Practical implementation of Least Squares Monte Carlo (tweaks and pittfalls)

The Longstaff-Schwartz LSM approach is nowadays ubiquitous(at least in the academic literature) in pricing path dependant derivatives. Up to now I have mostly worked with lattice methods. My ...
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1answer
735 views

Can the Heston model be shown to reduce to the original Black Scholes model if appropriate parameters are chosen?

Summary For Heston model parameters that render the variance process constant, the solution should revert to plain Black-Scholes. Closed from solutions to the Heston model don't seem to do this, even ...
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1answer
297 views

Asset-or-nothing Option Valuation in the Black and Scholes model

In standard Black-Scholes Model, compute the price of an asset-or-nothing put and asset-or-nothing call options. Write down the put-call parity relation between the asset-or-nothing call and put ...
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2answers
204 views

Price an option and find a replicating portfolio

I got stuck on the following question whilst learning about basic option pricing. A stock is valued at \$75 today. An option will pay \$1 the first time the stock reaches \$100 in value, which it ...
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1answer
78 views

Pricing options with two assets

I'm studying for a test and am stuck on this practice question: With interest rates equal to 0, two different stocks $S_1$ and $S_2$, both valued at \$1 today, can be worth \$2 or \$0.50 at some ...
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2answers
128 views

What information about the stochastic process is available from path-dependent options?

Assume the stock follows a process, which is defined by the following stochastic differential equation $$\frac{dS}{S}=r(t)dt+\sigma(S,t)dW,$$ so that the stock price process has local volatility. ...
5
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1answer
104 views

Model calibration to illiquid assets when pricing options with long maturities

Let us assume one is interested in pricing an option with a very long maturity (up to 20 or 30 years) on a liquid underlying. The market won't have liquid quotes for the higher maturities. Still you ...
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174 views

How are quants able to verify whether their calculated prices are any good

This question is related to the discussion on Model Validation Criteria However it appeard to be very high level to me and I would like to go more into detail. Not working at a pricing desk the ...
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2answers
148 views

Basket Option weight sensitivity calculation

I am looking to find/estimate the "greeks"/option price sensitivities/derivatives for a basket option situation. In specific the change in price of a put option associated with a change in weight of a ...
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1answer
142 views

binary tree options pricing model with dividend value - How should I discount the option at?

the expected value of the option given the next period up, down values is: $ Pexp = (p Price_{next, up} + (1 - p) Price_{next, down})/R$ where p is defined as $p = \frac{\exp(-r \times \Delta t) - ...
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8answers
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Why does implied volatility show an inverse relation with strike price when examining option chains?

When looking at option chains, I often notice that the (broker calculated) implied volatility has an inverse relation to the strike price. This seems true both for calls and puts. As a current ...
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3answers
208 views

Is it wrong to use 'real world' probabilities for option valuation?

Is it wrong to use 'real world' probabilities for option valuation, even when the market is not liquid enough to delta hedge the option? My instinct is that it is wrong, because the time value of ...
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2answers
857 views

Value of American Call vs Value of European Call when using implicit finite differences

I calculated values for put options (european and american) using the implicit finite difference method and compared them to black/scholes values. The values for american put options are higher than ...
3
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1answer
126 views

Derivation of the Stochastic Vol PDE

I'm trying to follow the derivation of the stochastic vol pde for an option price - as given in Gatheral (The vol surface), Wilmott on Quant Finance and many other places. As usual one starts off with ...
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2answers
471 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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0answers
56 views

Multivariate interpolation for estimating FDM in-between grid points

After implementing some FDM to price some option, there are gaps between our grid points that may be of interest. From reading around, it appears common to use bilinear interpolation to estimate ...
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1answer
136 views

How does Vega of a call/put behave under the Black-Scholes model?

I have two questions. I would prefer a reference if possible. Is the value of vega bounded for $\sigma\in [0,\infty)$? (I assume so, I imagine it goes to 0 as $\sigma$ go to infinity.) Are there any ...
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2answers
153 views

Time-zero price of two specific contingent claims

I am unsure how to start with the following problem. I have two contingent claims where contingent claim (1) pays $\int_0^T S_u du$ and contingent claim (2) pays $(\log S_T)^2$ at time $T$ Now I ...
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1answer
279 views

Price of a down-and-out call in terms of European call

If $EC(S_0, K, \sigma, r, T)$ represents the price of a European call option with strike $K$, expiry $T$, initial price $S_0$, volatility $\sigma$ and where the constant interest rate is $r$, then I ...
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2answers
302 views

Expected value of Black-Scholes

(Apologies for any formatting mistakes) Within the Black Scholes model, given that you are estimating the volatility from historical data - and all other parameters assumed exact - one usually ...
4
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2answers
294 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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1answer
91 views

Calculating deltas of call options?

From a continuous standpoint, I understand why an ATM call has delta = 0.5 and for ITM call, the delta approaches 1 since each move in the underlying corresponds to same unit of value change in call ...
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1answer
211 views

Arbirtage free price process question in Bjork's Arbitrage Theory in Continuous Time

I am currently working through questions in Bjork's Arbitrage Theory in Continuous Time. However, I am unable to solve the following question, 7.2 in the book. A solution would be greatly appreciated. ...
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1answer
135 views

Finite difference methods

I am simulating the price of a basket option with the help of equations from the report ...
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339 views

Finding Probabilities Using The Binomial Model

I was not able to find a similar question when searching, but if I've missed one please feel free to point me to it. Unfortunately the closest example in the textbook was not terribly helpful either. ...
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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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1answer
263 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
461 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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280 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
102 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 ...
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0answers
114 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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190 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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Where to find, d/l specific (OCC) historical Option data beyond the free 2 years [duplicate]

The OCC www.optionsclearing.com/‎ provides a nice breakdown for CBOE options data, however they only go back 2 years on any given day. Is there a good not-too-high-cost database one can recommend for ...
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971 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) ...