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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1answer
241 views

AmericanOptionImpliedVolatility - root not bracketed issue in QuantLib/R

I'm trying to compute an implied volatility -- I am trying to match real data I see in Yahoo finance which shows an IV of about 27%. My call in 'R' for the same params returns a root not bracketed ...
3
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5answers
167 views

Why don't real-world probabilities affect the price of a call in a 1-step binomial model?

I was a bit hesitant to post this question because it seems so basic...but I wasn't able to figure it out on my own. Say we setup a one-step binomial tree with $S_0=100$, $S_u=110$ and $S_d=90$, ...
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1answer
145 views

Notional Value in Equity Options

I have calculated the NPV of an Equity option and need to account the notional for it and have issues understanding the NPV <-> notional relation. Example: Strike price 100 Spot rate: 107.41 NPV ...
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0answers
42 views

Cumulants of variance gamma with stochastic arrival (VGSA) model

The characteristic function of the VGSA model is defined as a specific parameterization of the characteristic function of the CIR (Cox-Ingersol-Ross mean reverting process) time-change: $ \mathbb{E}e^...
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0answers
38 views

Compute stock price probability distribution from option data (IB method & negative probabilities issue)

I'm using a procedure as described in the interactive brokers article here (https://www.interactivebrokers.com/en/index.php?f=5910&ns=T) to compute a probability distribution from option (call) ...
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1answer
127 views

Estimating profit/loss of a Gold Futures option using Theta and Gamma

HELP! I am trying to find how much the underlying price of a gold futures option must move in order to breakeven on owning an option for a day. I was hoping someone versed in pricing options could ...
0
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1answer
123 views

How to calculate confidence interval for option price?

I model option prices for European call using Monte Carlo method. What is the proper way to calculate the confidence interval? A. -> Calculate the payoffs (there will be number of zeros as some ...
4
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2answers
275 views

How to trade leveraged ETFs

Leveraged ETFs (LETFs) are known to lose value over time due to the "volatility decay" effect. What're the most common strategies for trading LETFs to take advantage of this volatility effect? Also, ...
1
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1answer
84 views

Double no touch option with four barriers

The double no touch (also known as a range binary) is an option with two American barriers. You define one barrier above the underlying asset and one below it. If during the option's lifetime the ...
6
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0answers
200 views

How should option prices differ when using the Heston versus the Black-Scholes model?

I am running Monte Carlo simulations for a European Call using Heston Model and I am trying to compare them with prices calculated using Black-Scholes formula. I am not quite sure if the prices I get ...
1
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1answer
67 views

PPPN: premium with real market data

A few days ago, I posted a question about PPPN's (partially principal protected notes), which can be found here:PPPN: participation rate, stocks and premium. A PPPN in short is a structured product ...
7
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1answer
511 views

Arbitrage opportunity interview question

I have seen this interview question mentioned in a couple of places: There are three call options on the market, with the same expiry and with strikes 10, 20, and 30. Suppose the call option with ...
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1answer
54 views

does local volatility make any sense when I only focus on vanilla option?

can someone explain me the usage of local volatility? details will be appreciated. Is it of any importance when I now are doing market-making? Please do not laugh at me as I am totally new in this ...
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2answers
77 views

zero coupon problem calculus

I encounter a problem: do we have the following equality : $B(0,T_{i})e^{\int_{0}^{t}r_{s}ds}=B(t,T_{i})$ and if yes why because I am stuck with this ... I try to use that : $B(t,T_{i}) = B(0,T_{i})e^...
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2answers
102 views

Analysis of exercising a call option early

Most options traders sell their call options early instead of exercising them, as you would make a bigger profit this way due to being able to salvage some remaining extrinsic value. For example: ...
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0answers
62 views

Determining Strike Price given stock price and option price

I am having a bit of trouble with this problem: Say the current price of a stock is 100 and an individual purchases an in the money option for 10. Using that info, how can you determine what the ...
1
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1answer
127 views

how to do interpolation in the term structure of volatility surface?

everyone~ I am a newbee in the quantitative finance and I meet a problem in working out an equity option volatility surface. We use the reasonable market data to derive the implied volatility, then ...
2
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1answer
98 views

Implied Volatility in Heston Model

recently I started reading the interesting book about option pricing in the stochastic volatility world from Lewis. He gives very interesting and detailed insights about this topic in general. However ...
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1answer
78 views

Why do banks offer options? [closed]

I have only taken one introduction class in finance. However we came along opinions, their pricing, etc. We only contemplated being the buyer of a option. If everything works for you apparently you ...
2
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2answers
129 views

$E[F_T] = F_0 \ \rightarrow \ \text{or} \ \leftarrow \ p = \frac{1-d}{u-d}$?

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 ...
3
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2answers
249 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 ...
1
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1answer
156 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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4answers
240 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
35 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 ...
2
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1answer
89 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
121 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
76 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 ...
1
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1answer
32 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: $E_{Q}[(...
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1answer
63 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 Black-...
2
votes
3answers
72 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 ...
7
votes
2answers
231 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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0answers
13 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 ...
1
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1answer
94 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 ...
2
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0answers
82 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
74 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 unzipped)...
2
votes
2answers
228 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 ...
3
votes
3answers
141 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 $0 < t < T$. ...
3
votes
3answers
237 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 ...
0
votes
1answer
82 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 Problem:...
2
votes
2answers
120 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 in-...
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0answers
12 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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0answers
223 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
83 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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3answers
165 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 ...
0
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1answer
64 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
103 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 ...
2
votes
1answer
126 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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0answers
104 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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3answers
188 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 ...
3
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2answers
117 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 ...