Questions about models for the valuation of option contracts.

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22
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634 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 ...
7
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0answers
284 views

Transformation of Volatility - BS

I have recently seen a paper about the Boeing approach that replaces the "normal" Stdev in the BS formula with the Stdev \begin{equation} \sigma'=\sqrt{\frac{ln(1+\frac{\sigma}{\mu})^{2}}{t}} ...
6
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0answers
124 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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0answers
234 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
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0answers
479 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
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0answers
173 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 ...
3
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0answers
87 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
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0answers
40 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
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0answers
202 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
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0answers
278 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
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0answers
46 views

Approximate asian geometric option with Heston

I am trying to implement Theorem 1 from this Journal in RStudio. The journal says the it is possible to find a approximate price of a geometric asian option in a Heston setup this way: ...
2
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0answers
49 views

why many option contract price less than minimum boundary price?

I downloaded data from NSE(National Stock Exchange) website regarding closing price of European Call Option written on Index. From standard textbook, I read that option contract must satisfy $C(t) ...
2
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0answers
58 views

Hedging - calculating option prices using implied volatility surface

To hedge a strategy is it accurate "enough" to price an option using an implied vol curve vs moneyness (strike/spot) assuming sticky delta? The moneyness can be read off the chart, its corresponding ...
2
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0answers
33 views

replicating strategy three step binomial

I am having some trouble setting up a replicating strategy for a call option with a three step binomial model (discrete). I have no trouble doing this in a two step binomial model by backward ...
2
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0answers
120 views

negative transition probabilities in the heston model

I've been trying to implement a bivariate tree for pricing american options with the heston model in R using the paper of Beliaeva and Nawalkha ...
2
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0answers
48 views

Discretization Schemes

I am working with two correlated SDE's and I was wondering if I could use two different discretization schemes for them. Is there maybe a reference of this being done? And can something be said about ...
2
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0answers
65 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 ...
2
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0answers
101 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 ...
2
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0answers
166 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 ...
2
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0answers
79 views

Any thoughts on how Warren Buffet's B of A warrants might be “marked-to-market” by either counterparty?

It's not too long since Berkshire Hathaway got its 10-year warrants in Bank of America alongside its \$5 billion purchase of preferred stock. At the time I saw some discussion about the value of ...
2
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0answers
135 views

How to find the upper bound of a digital option given some market data?

Given the price of a call equals to 5 with Strike 100, please find the upper bound (sup) of the digital option with strike 105. I am not sure about the solution, but I write the condition like this, ...
2
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0answers
204 views

Tian third moment-matching tree with smoothing - implementation

I was wondering if someone has an implementation of the Tian third moment-matching tree (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1030143) with smoothing in code (e.g. c++, vba, c#, etc.)? ...
1
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0answers
37 views

Use of Black-Scholes Model on Guaranteed Fund Investment

I am stuck with a revision question at home on Black-Scholes pricing model. The question is on a fund manager selling one unit of the fund to a customer for S(0) at time 0 and then guaranteeing at ...
1
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0answers
45 views

How to apply the chain rule for partial derivatives to transformations?

I'm currently working to solve the Black-Scholes model partial differential equation (it's a model for a.o. stock option prices). The Black-Scholes equation for a calloption C(S,t) is given by $ ...
1
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0answers
62 views

Value of an option to exchange an asset for another

I'm working out the examples in the paper "Changes of Numeraire, Changes of Probability Measure and Option Pricing", corollary 3. An option of exchanging asset 2 against asset 1 at time T, its time-0 ...
1
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0answers
267 views

Black Scholes - how to calculate delta with a vol skew

I am trying to calculate the delta of an option at different strike prices where the underlying has a pronounced implied volatility skew in order to correctly hedge an options strategy. Researching ...
1
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0answers
70 views

Underlying changes impact on implied volatility

What are some valid techniques that can be used to simulate how changes in the underlying are most likely to impact implied volatility along with the skew of all strikes for options with the same ...
1
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0answers
245 views

The option values are different from two r package - foptions,rquantlib

The results are very different.I know the code from quantlib and the result of quantlib seem right(close to market price). Is there anyone know why the value from fOptions is so large or fOptions used ...
1
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0answers
145 views

Pricing binary options with kernel density estimation

Suppose I have a large enough set of prices of an asset, from which I can extract the following function: $f:T\to\mathcal{D}$, where $T$ is a fixed finite set of time intervals (say, 1 minute, 2 ...
1
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0answers
135 views

A question about pricing convertible bond with two different underlying assets

I have a question regarding the pricing of convertible bond. If I value the convertible bond with two different underlying assets, how can I incorporate two volatility and the correlation in the ...
1
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0answers
99 views

American Swaption Pricing with PDE discretization

So I am still trying to price an american swaption. (MC approach here: American Swaption Pricing with Monte-Carlo method) I've found in Paul Wilmott, The mathematics of financial derivatives, a PDE ...
1
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0answers
56 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 ...
1
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0answers
312 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: ...
1
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0answers
124 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 ...
1
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0answers
525 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?
1
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0answers
205 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 ...
1
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0answers
222 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 ...
0
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0answers
47 views

Examples for the option model validation

When implementing a code for the new model, even if it provides sensible price, it is still a good idea to compare it against some benchmarks, even in the special case of constant volatility ...
0
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0answers
33 views

Can a large OpenInt of calls cause a stock to go down?

I read forum post from another site. Which stated... ...
0
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0answers
35 views

What's the risk-neutral expectation of the arithmetic average of stock price?

All Black-Scholes assumptions apply ($y$ is yield): what's $E(A_T), E(A_T^2)$ and $Var(A_T)$ where $A_T=\frac{\int_0^T S_tdt}{T}$ is the continuous-sampling arithmetic average of the stock price ...
0
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0answers
71 views

Black-Scholes formula with deterministic interest rate and dividend yield

Does any one have the Black-Scholes formula for a European call with time-dependent but deterministic interest rate and dividend yield ?
0
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0answers
42 views

Benchmarking option pricing under stochastic interest rates

I priced a long-term option (10 or 20 years) using two different models: one assumes constant interest rates, the other assumes stochastic interest rates. Is there a way (e.g. a benchmark) to ...
0
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0answers
45 views

“Hedging” a put option, question on exercise

I have a question on the following exercise from S. Shreve: Stochastic Calculus for Finance, I: Exercise 4.2. In Example 4.2.1, we computed the time-zero value of the American put with strike ...
0
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0answers
72 views

Vanna-Volga Adjustment

I'm reading Uwe Wystup's "FX Options and Structured Products" to understand Vanna-Volga pricing, which, in his book Chapter $\S3.1$ is called "The Trader's Rule of Thumb". I generally got the idea ...
0
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0answers
27 views

Multinomial Representation Theorem

In the context of pricing models, the Binomial Representation Theorem (BRT) tells us if we have a binomial price process $S$ that is a $\mathbb{Q}$-martingale (MG), and any other $\mathbb{Q}$-MG $M$, ...
0
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0answers
47 views

Binomial function use in Bezier smoothing

I am using the Bezier method to smooth option volatility curves, which utilised the binomial distribution. Is someone able to clearly explain the interpretation of the binomial distribution in the ...
0
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0answers
35 views

Invoice Discount pricing model

I was wondering whether there exist pricing models in particular for Invoice Discounting contracts and short-term financing solution where credit risk plays a major role. Specifically, assuming that ...
0
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0answers
28 views

Price a put option on a CPPI

I want to price a put option on a CPPI using Monte Carlo. I have found so far this article which prices a call on a CPPI. I was wondering if I could use the put/call parity here, and and if so, how ...
0
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0answers
6 views

Will a back month leg in call calendar lose value if underlying goes down

If I buy a call calendar and underlying drops 5%, the front month short call will get further out of money and will lose value, resulting in a gain since I am short the front month option. What about ...
0
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0answers
39 views

Why does the OTM call sometimes have a higher theta than the ATM call?

In this AAPL option chain on Mar20 call options, the OTM calls have a slightly higher theta than the ATM calls. Why is this? Is not time value(and thereby time decay) supposed to be highest for ...