A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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76 views

$E[F_T] = F_0$, $p = \frac{1-d}{u-d}$ --> Which implies which?

From Ch 12 in Hull's OFOD, we compute the risk-neutral probabilities for a futures contract: Later in Ch 17, futures options are valued, and we have the same result: In relation to ...
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226 views

Pricing when arbitrage is possible through Negative Probabilities or something else

Assume that we have a general one-period market model consisting of d+1 assets and N states. Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option, with ...
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2answers
101 views

Delta Hedging for 2 Factor Models

If the value of an option at Maturity is what is the off-setting position you take for X and Y, if you are i)Long Call of the option ii)Short Call of the option iii)Long Put of the option iv)Short ...
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200 views

European Call Option Delta Upper Bound

For a pure equity process (with interest rate, dividend, etc., being zero) not necessarily the geometric Brownian motion, is the delta of a European call option always no higher than $1$? I am NOT ...
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0answers
27 views

hedging of a spread option with call

We have 2 underlying $S^{1}$ and $S^{2}$ with BS dynamic under the risk-neutral measure (r constant...) I found the (big) PDE satisfied by the price function $u(t,x,y)$ of a call spread whose payoff ...
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1answer
62 views

Under what circumstances Veta is positive?

In general, as the option moves towards expiry, its vega is decreasing. Are there circumstances where the veta, i.e. the sensitivity of vega with respect to time, is positive, that is when vega is ...
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3answers
97 views

Greeks for binary option?

How to derive an analytic formula of greeks for binary option? We know a vanilla option can be constructed by an asset-or-nothing call and a cash-or-nothing call, does that help us? Wikipedia states ...
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1answer
56 views

pricing with implied volatility surface

I am a newbee in Quantive finance. supposing I calibrate a smoothing implied volatility surface with cubic spline now. A minute later I want to price K=100,t=1 option, can I just find the point on ...
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1answer
21 views

no arbitrage condition for paylater option

a paylater option has the folowing payoff: $(S_{T}-K)_{+}-P1_{S_{T}>K}$. To determine the fee P that the option holder must pay, we must write the non arbitrage condition. Why is it this: ...
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1answer
53 views

How to estimate the price of a European call when the underlying is not tradable?

Assume you have a vanilla call on an underlying $S$ with strike price $K$ and expiry at time $T$. Let's say that $S$ follows a GBM with volatility $\sigma$. In general, one would use the ...
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3answers
69 views

How would I exploit arbitrage if risk-neutral pricing doesn't hold? (Option Pricing)

We are just learning about binomial option pricing, and how the up-factor and the down-factor must match the risk-neutral price. p * u + (1 - p) * d = continuous risk free rate compounded CRR ...
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187 views

How to price an option allowing to change a call into a put?

A recruiter asked me this question: Suppose you have the following contract: a call option with maturity T = 2 years the possibility to change this call into a put at t = 1 year What is the price ...
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11 views

Option style with grant date

The following option exercise style is somewhere between American and European: There is a fixed grant date $N_1$ at which you determine at which date $N_2>N_1$ the option will be exercised. So ...
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1answer
74 views

QuantLib: New Instrument derived from VanillaOption + PricingEngine that must work for both VanillaOption and the derived class

The derived class is a Vanilla Option on a Future and I need to specify the expiry of the underlying future which is in general different (later) than the expiry of the Vanilla Option. I have ...
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0answers
64 views

Example of optimal delta hedging in G. Barles, H.M. Soner option pricing paper

There is a paper Option pricing with transaction costs and a nonlinear black-scholes equation by Guy Barles and Halil Mete Soner. And there is a section about optimal (delta) hedging, which I do not ...
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0answers
67 views

Match different option high frequency databases

I downloaded the “E-mini S&P 500 (Dollar) Options for 1/10/11” Top-of-Book (BBO) data. If you are interested you may download the data from the following link (approx. 80MB zipped and 1GB ...
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2answers
224 views

Pricing options under a specific framework

I have a specific framework in mind and I would like to value options under this framework. I am not sure whether a closed form solution exists or Monte Carlo methods would work. The framework I have ...
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3answers
135 views

How to price a path dependent exchange option using?

Assume you have two stocks $S$ and $P$ so that at initial time $t = 0$: $S_0 > P_0$. You bought an option which pays off $S_T - P_T$ as long as $S_t > P_t$ through the time $0 < t < T$. ...
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0answers
86 views

Option greeks vs Position greeks

I know that when it comes to delta, you would calculate your position delta (of a stock position) as follows: option delta * position size * 100 For example if I ...
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1answer
70 views

Calculating the volatility for Black Scholes

The following problem is from the book by Hull. I did it but I am not sure it is right. I am hoping that somebody here can tell me if I did it right and if not where I went wrong. Thanks Bob ...
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2answers
70 views

what is exercise frontier in option pricing

What's exercise frontier in option pricing? It kept popping up but I was never fully introduced to the concept. Follow up question: And is the optimal exercise time the first time the option is ...
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0answers
11 views

where can I find OPRA data? [duplicate]

Where can I find OPRA data. Here are a few criteria 1. Preferably free or for a small price 2. Supports quant api on cloud (so I dont number crunch on my computer) 3. Good reputation company
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105 views

Formula behind pandas.Options() implied volatility

I noted that implied volatility (IV field) from pandas.Options class is very different (especially, for out of money options) than what I compute with Black-Scholes model. (risk free rate is pulled ...
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1answer
55 views

Call and Put Prices Equal at Forward Price - Why?

Consider a European call and put with values $C_t$ and $P_t$, respectively, under the Black-Scholes model. By put-call parity, $$ C_t - P_t = S_t - Ke^{-r(T-t)} $$ for expiration time $T$. Note if ...
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2answers
99 views

delta hedging strategy for OTM option

Wondering how you would think about the following thought experiment - suppose you sell an OTM call option and plan to implement a delta hedging strategy whereby if the price of the stock were to ...
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1answer
52 views

Basic Metrics for Option Trading Limits

Imagine a trading house that trades options in a modest way, and is looking for simple but effective metrics over which trading option limits will be set. Some random thoughts: 1) VaR is not ideal, ...
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1answer
88 views

Does the fact that volatility is not constant imply existence of skew?

I had a question regarding the existence of the volatility skew. I've tried researching it a fair bit and I come across a few different explanations: 1. Market participants like buying downside puts ...
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1answer
107 views

What should be the sign of greek letter $\rho$?

I'm reading the book Risk Management and Shareholders Value in Banking by Resti & Sironi. I quote a paragraph from the book (Chapter 5, appendix): The derivative of an option’s value with ...
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56 views

Turnbull & Wakeman Asian - not Edgeworth?

My understanding is that Turnbull & Wakeman derived an approximation formula for continous arithmetic Asian option using Edgeworth series by matching the first two moments. However, in the book ...
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81 views

Calculating historical implied volatility

I know that each individual option has it's own implied volatility, but how do you go about calculating the overall implied volatility for an underlying? For example when someone sais the IV of a ...
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2answers
83 views

Sobol numbers in monte Carlo simulation

I wanted to figure how how much faster the Sobol quasi random numbers convergence to the B&S call price compared with pseudo random numbers. To generate the Sobol numbers I used the randtoolbox in ...
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1answer
51 views

Is it possible to detect a belief that a security will peak and then decline by analyzing American options pricing?

Please forgive me if this is a dumb question. I know only the basics of options and their valuation, and this is a question I've wondered for some time without being able to find a satisfactory answer ...
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59 views

Delta Volatility Surface Usage to value the option

I always find myself in the unknown charted territory when it comes to non-Linear Instruments. I come across the scenario, How to value the option using Delta Vol surface? Example I have CME traded ...
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15 views

Methods Available for Derivative Pricing in Mathematica? [closed]

I am using Mathematica to price options (built in functions, no need to reinvent the wheel, right?). In the documentation, the Binomial method is used as an example of specifying a non-standard ...
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1answer
98 views

Understanding skew of SPX - Why does IV of OTM puts increase with strike?

I've been trying to understand the skew I see when looking at the skew of SPX. Here is a snapshot today from thinkorswim. I understand why IV increases for ITM puts -- namely because there is a ...
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4answers
147 views

Model Price vs Market Price in terms of Fair Price (Options)

Before I start: Ok, this is something I investigated for a fair amount of time and my question is semi-academic. To simplify, I will introduce the short bit (TLDR) of my question and then lay out ...
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1answer
287 views

How to use a change of numeraire to price this option?

I recently asked this question regarding how to price an option with payoff: $$\text{Payoff}_T = (A_TR_T - A_T \lambda)^+ $$ Let's assume for generality that $A_t$ and $R_t$ are GMB's: $$dA_t = ...
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1answer
120 views

What is the correlation between these two functions of GBMs?

Let's say that I have two correlated GBMs: $$dA_t = A_t \sigma^A dW^A_t$$ $$dR_t = R_t \sigma^R dW^R_t$$ $$dW^R_t dW^A_t = \rho dt$$ I am trying to price a derivative which payoff at time $T$ is: ...
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2answers
97 views

Computing loss of Call / Stock Purchase

A seller of an European Call, can, subjectively have unbounded losses. This loss may be mitigated by buying the stock (covered call). In this case,, the loss will be bounded at A. How would one ...
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2answers
569 views

Options pricing exercise - American call option on a futures contract

I am confused by a particular exercise I am doing right now, I am hopeful that someone can walk me through as to how to solve it. I further hope the question is not considered too basic for this ...
3
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3answers
123 views

Implied volatility of a complex options position

Assume I have a "complex" options position like a straddle, strangle, or iron condor. In other words, several options traded together as a single position against one underlying asset (not a basket ...
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1answer
77 views

What is more likely effect to call and put prices, respectively, if the stock price decreases by$1?

The current stock price is \$80.Call ,and ,put, options, with ,exercise ,prices, of $50 and 3 days to maturity are currently trading. What is more likely effect to call and put prices, respectively, ...
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44 views

Logic between options and risk free rate [closed]

What is the relationship between put option price and risk free rate? And between call options price and risk free rate? Explain the logic? No calculation.
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0answers
21 views

Financial Derivative, European Option [closed]

Market Prices for European put and call options on ABC stock are as below: Call = $4.5 Put = $6.8 Exercise Price, X =$70 Risk Free Annual Compounded rate r = 5% Time to expiration T = 139 days ...
2
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0answers
30 views

Equity protection and butterfly certificates pricing

Certificates issued by famous industry names are usually made up by a combination of a fixed income instrument and some vanilla and exotic options. I am looking for something which explains: how to ...
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0answers
32 views

Gil-Palaez Inversion Formula in Black Scholes world

I am trying to calculate numerically the price of a plain vanilla call through Fourier Transform, by applying the Gil-Pelaez formula. More precisely, we have that C(K)=S0*Π1-Kexp(-rT)Π2 where ...
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59 views

Are there academic papers on the 'term structure' of adverse selection for futures and options?

By term structure I mean a non-stationarity in the pattern of intraday adverse selection as a given instruments approaches its expiry. Note that I am interested in the adverse selection on the ...
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603 views

Why does it take so many lines of code to price even the simplest of options with QuantLib

I have been looking at QuantLib I am trying to figure out why I need to write so much boilerplate code even when pricing the "simplest" of European Options using the analytical Black-Scholes formula ...
4
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1answer
60 views

When are ES E-mini future options issued?

Since options lose 2/3 of their time value in the second half of their lifespan, it makes sense to be aware of when an option was issued. What are ways of figuring out when ES futures options have ...
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2answers
65 views

put call parity for futures options derivation in Hull

In Hull, the following derivation of PCP for futures options: What confuses me is that it is stated that the payoff of the long futures is $F_t-F_0$. The footnote states: the analysis assumes that ...