Questions about models for the valuation of option contracts.

learn more… | top users | synonyms (1)

4
votes
3answers
251 views

How to hedge a derivative that pays the reciprocal of the stock price?

1) Suppose S is the stock price, how to hedge a derivative that pays $1/S_t$ at time $t$? 2) Suppose there will be a dividend of amount $d$ between $t$ and $T$, how to hedge a derivative that pays ...
4
votes
1answer
186 views

Analysis of Unbalanced Covered Calls

Hello I am doing an analysis on covered calls with and extra amount of naked calls. Ignore the symbol and current macroeconomic events. I couldn't find any reference to this strategy (unbalanced is ...
4
votes
0answers
222 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 ...
4
votes
2answers
3k 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 ...
4
votes
0answers
475 views

ATM volatility versus OTM volatility and directional standard deviation

The forward instrument vol curve is skewed to the downside (50 delta risk reversal, 25 put, 25 call) were trading several ticks to the put). Is there a smaller standard deviation (in price terms) to ...
4
votes
0answers
169 views

Use of Local Times in Option Pricing

I know two applications of local time in option pricing theory. First, it allows a derivation of Dupire's formula on local volatility in a neat way (i.e. without resorting to differential operator ...
4
votes
1answer
109 views

How to price a futures spread option?

Let's say I have two futures contract $F_1(0,T)$ and $F_2(0,T)$ on two different correlated underlyings. If I assume that both underlying follow a GBM with volatility $\sigma_1$ and $\sigma_2$ ...
3
votes
4answers
2k views

Ways of treating time in the BS formula

The Black-scholes formula typically has time as $\sqrt{T-t}$ or some such. My questions: What is the granularity of this? If we treat $t$ as the number of days, then logically on the day of expiry, ...
3
votes
3answers
117 views

Arbitrage bounds for Black-Scholes

In some implied volatility code I came across, there is a check to ensure there is no violation of the arbitrage bounds based on the inputs to the method. For the call option, if $$P < 0.99 * ...
3
votes
2answers
101 views

Black Scholes: How does it help to transform uncertainty and still not be able to calculate a fair price?

Recapitulating the history of Black-Scholes: Nobody knows the fair price of options. Revolution: BS! You put in all the parameters and get a price -> A Nobel Prize for that one! Wait: Nobody knows ...
3
votes
2answers
388 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 ...
3
votes
2answers
366 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
votes
2answers
221 views

Does higher vega imply higher IV and vice versa

If an option A has higher vega than option B, does that also mean that A has a higher IV than B? I understand that by definition, a higher vega means that A's price is more sensitive to its IV than B. ...
3
votes
2answers
68 views

Hedging portfolio and extraction PDE of SV model with stochastic interest rate

How can I extraction this PDE \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + \frac{1}{2}P_{\sigma ...
3
votes
1answer
169 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 ...
3
votes
1answer
3k 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 ...
3
votes
1answer
311 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. ...
3
votes
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 ...
3
votes
1answer
146 views

Data Selection for Empirical Pricing Kernel Estimation (Stochastic Discount Factor)

I want to estimate an empirical pricing kernel for an index. Hence, I need to estimate a physical and risk neutral density. For estimating the physical density, only the index data in an observed time ...
3
votes
1answer
260 views

SABR calibration: simple explanation and implementation

I would like to learn more about the SABR model and ho it is used in modeling smiles in equity, FX and rates markets. How would you explain the process and its implementation in simple steps? Any web ...
3
votes
2answers
309 views

Pricing an american style option on a bond future

what is the good way to pricing american option on bond future? From bonk fixed income securities 3rd by Tuckman, I understand how to pricing European option on bond future, but I still have no clue ...
3
votes
1answer
142 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 ...
3
votes
1answer
142 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 ...
3
votes
1answer
421 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 ...
3
votes
1answer
1k 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, ...
3
votes
2answers
154 views

What mathematical characteristics are required from the asset price process in order to stay within the RNP framework?

I'm currently doing a course in derivatives pricing and I'm having some trouble wrapping my head around the sweet spot where theory meets reality in terms of Risk Neutral Pricing. I know that the ...
3
votes
1answer
289 views

Which approach is better for modeling option exercise strategies, rational or behavioral?

This question is most relevant to the evaluation of embedded options, such as the refinancing option granted to borrowers in the mortgage and bank loan markets, or the call option present in some ...
3
votes
1answer
349 views

European turbo warrants

Totally new to the world of quant finance, so perhaps this is an odd question... Does there exist an American equivalent to the German style "knock out zertifkate"? (The name might be slightly ...
3
votes
1answer
45 views

Numerical example of how to calculate local vol surface from IV surface

I'm looking for an excel example (not a copy of Dupire's eqn) of how to convert an IV surface to a local vol surface. If unsuccessful I'll work through Dupire's eqn but would be helpful to look at an ...
3
votes
2answers
120 views

Stock Returns Distribution in Heston Model

There is a paper by Dragulescu and Yakovenko (DY) in 2002 proposing a pdf for the stock returns in the Heston model. However, in a paper by Daniel, Bree and Joseph, they actually perform statistical ...
3
votes
2answers
127 views

Time-independent local volatility

Suppose somebody provides us with a surface of European call prices $C(\tau,K)$ where $\tau$ stands for time-to-maturity and $K$ for the strike. By Dupire's results, there is a unique local volatility ...
3
votes
1answer
132 views

Literature on Empirical Option Pricing

When I started combing through the literature I was astonished about how little the option pricing models are tested against market data and benchmarks are limited. The main barrier is of course ...
3
votes
1answer
144 views

Fitting stochastic variance distributions to index return data

I want to calculate option prices based on a realistic distribution of the underlying. The underlying is a liquid index such as Eurostoxx50. I think of two aproaches, both of them incorporate ...
3
votes
1answer
192 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 ...
3
votes
1answer
157 views

Finite difference methods

I am simulating the price of a basket option with the help of equations from the report ...
3
votes
1answer
448 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 ...
3
votes
1answer
475 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 ...
3
votes
1answer
101 views

Distribution of Black Scholes call option price at time 0<t <T

Does anyone know how to find the probability law (distribution) under P* of a Black Scholes Call Option price $C_t$ for $0 < t < T $? (Under P*, $ dC_t = \frac{\partial c}{\partial s}\sigma S_t ...
3
votes
1answer
303 views

a good book on option pricing from theoretical and practical aspect

This is the situation someone I know is in: She has good understandings of stochastic calculus and the very basics about black-scholes and binomial model, but nothing more. Her background is in ...
3
votes
1answer
174 views

Parameter estimation using martingale measures - include real world data?

Please note: I posted this in nuclearphynance first, but didn't get any replies. For desks which sell exotics it is common practice (as far as I know it) to calibrate the model (Stochastic ...
3
votes
0answers
78 views

How can a beginner trader make use of 'volatility of volatility'

For a beginner option trader in equity options, how can he use this metric that is provided by his broker/data vendor? How can he use this metric to gain an added understanding of the option ...
3
votes
0answers
36 views

How to price lookback american option when its payment is distributed during its life

I would like to price a floating strike american lookback with a particular feature: I don't want to charge upfront the client, rather I would like to insert a "running fee", some sort of a dividend. ...
3
votes
0answers
194 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 ...
3
votes
1answer
183 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 $- ...
3
votes
0answers
272 views

Pricing with collateral

I have been confused about many things concerning the princing of securities with collateral. We can prove that today's price of a security( fully collateralized and within the same currency) is the ...
2
votes
4answers
3k 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 ...
2
votes
2answers
174 views

Is it fair to assume $(ud=1)$ in the binomial tree option pricing model?

I have discussion with my colleague on why a general assumption $$ud=1$$ in binomial tree option pricing model would be necessary? I take it a simplification of the problem, otherwise, there will be ...
2
votes
3answers
2k views

Why are exotic options most popular in FX?

I was reading Derman's latest blog post on Vanna Volga pricing, which, according to the linked Wikipedia article, is used mostly for pricing exotic options on foreign exchange (FX). This Willmott ...
2
votes
2answers
4k views

How do I estimate convergence in monte carlo methods?

I am experimenting with Monte Carlo methods. I'd like to measure/estimate convergence with a graph/chart. How do I do that? Can anyone please direct me to relevant documentation/links or even give me ...
2
votes
2answers
164 views

Why do we need $dS_t=r S_tdt+\sigma S_tdW_t^Q$?

Suppose $S_t$ is the stock price and follows the dynamics $$dS_t=\mu S_tdt+\sigma S_tdW_t$$. According to Girsanov, we can apply change of measure and obtain $dS_t=r S_tdt+\sigma S_tdW_t^Q$, this ...