# Questions tagged [options]

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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### Calculate strike from Black Scholes delta

I have a list of deltas and their corresponding volatilities in an FX market but I want to go from delta to strike price. In this Question similar problem is being discussed How can I calculate the ...
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### What causes the call and put volatility surface to differ?

I currently have a local volatility model that uses the standard Black Scholes assumptions. When calculating the volatility surface, what causes the difference between the call volatility surface, ...
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### How to exploit calendar arbitrage?

Say we are looking at European Call options in a toy environment with zero deterministic interest rates, a stock paying no dividends, no repo rates etc... Let $C(T,K)$ be the price of a call with ...
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### Modeling Call Price w.r.t. Strike w Models that Capture Vol Smile

I am trying to model $C(K)$, the price of the call $C$ as a function of strike $K$. Because this is tied to Prob ITM - and in fact the probability density function of that particular expiration (https:...
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### Barrier option (autocallable) Vega profile

I have a question about the Vega profile(graph) on an autocallable option. Generally for a regular option, the vega graph looks like a normal (kinda normal) distribution with the vega highest at-the-...
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### Implied dividend estimation

I am looking at two different ways of estimating the expected / implied dividends from market data. 1. Dividend futures I know that this asset class is not very liquid and might not be ...
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Suppose that we model a price $P_t$ to evolve per $$\frac{dP_t}{P_t}=\mu dt+\sigma dW_t$$ for $\mu\in\mathbb{R}$ and $\sigma>0$. The unique strong solution to this diffusion is $$P_t=P_0e^{(\mu-\... • 155 2 votes 3 answers 960 views ### Do basket options have a closed form valuation formula? Suppose I'm simulating a European call option on a basket consisting of N stocks with slightly varying volatilities but all other parameters remain the same. From the perspective of an estimate, it ... • 21 5 votes 1 answer 4k views ### Option prices in Bates SVJ model? In this [post] discussed the European put and call price formulas under the Heston Stochastic Volatility model. There exists an important extension of Heston model to include diffusion jumps, known ... • 5,669 4 votes 3 answers 702 views ### Probability of an Option maturing In-the-money vs. Volatility How will the probability of an option ending up in the money change if the volatility of the underlying stock increases? Intuitively, I think the answer to this is that if volatility goes up the ... • 2,262 0 votes 0 answers 251 views ### Exotic option arbitrage Suppose an exotic European option has a sub hedging (price being lower than the target) portfolio of vanilla European options all with the same expiry as the exotic option. The sub hedging portfolio ... • 2,511 11 votes 1 answer 5k 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 ... • 113 13 votes 3 answers 8k views ### What really is Gamma scalping? How does Gamma scalping really work? It seems there is no true profit scalped. If we look at the simplest scenario, Black-Scholes option price V(t,S) at time t and the underlying stock price at S... • 2,511 16 votes 2 answers 20k views ### Gamma Pnl vs Vega Pnl Why does Gamma Pnl have exposure to realised volatility, but Vega Pnl only has exposure to implied volatility? I am confused as to why gamma pnl is affected (more) by IV and why vega pnl isnt affected ... • 2,262 17 votes 9 answers 9k views ### Why the expected return rate of a stock has nothing to do with its option price? OK, I admit that this is a frequently asked question. But I couldn't find a satisfying answer after I read the explanations of books, went through the derivations of B-S formula, and searched answers ... • 271 21 votes 3 answers 6k views ### Is there a popular curve fitting formula of options skew vs strike price or vs Delta? I was trying to build a options trading/optimization system. But it often gets more inaccurate as it scans through the far from ATM options because, you know, options skews. That is because I did ... • 311 21 votes 3 answers 8k views ### Is there an all Java options-pricing library (preferably open source) besides jquantlib? I am looking for an all-java implementation of black scholes, preferably open source. I found jquantlib and quantlib (C++). Any other recommendations? The jquantlib site seems to be down. I'd prefer ... • 249 13 votes 2 answers 3k views ### What are the main flaws behind Ross Recovery Theorem? Stephen Ross’ new paper claims that it is possible to separate risk aversions and historical probabilities if the Stochastic Discount Factor is transition independent using Perron-Frobenius Theorem. ... • 1,856 8 votes 4 answers 9k views ### Basket option pricing: step by step tutorial for beginners I would like to learn how to price options written on basket of several underlyings. I've never tried to do it and I would appreciate if you can provide some documents, papers, web sites and so on in ... • 2,046 9 votes 2 answers 939 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 ... • 617 17 votes 7 answers 6k views ### Why do institutional Traders prefer Short Selling instead of Buying Puts? Why is it more common for Institutional Traders to short sell stocks when they have a bearish stance instead of Buying Puts? The limited loss potential of Buying Puts seems like a better choice. • 355 24 votes 6 answers 3k views ### Setting the r in put-call parity? Put-call parity is given by C + Ke^{-r(T-t)} = P + S. The variables C, P and S are directly observable in the market place. T-t follows by the contract specification. The variable r is ... • 2,059 14 votes 3 answers 7k views ### How does volatility affect the price of binary options? In theory, how should volatility affect the price of a binary option? A typical out the money option has more extrinsic value and therefore volatility plays a much more noticeable factor. Now let's ... • 1,822 14 votes 2 answers 7k views ### How to extrapolate implied volatility for out of the money options? Estimation of model-free implied volatility is highly dependent upon the extrapolation procedure for non-traded options at extreme out-of-the-money points. Jiang and Tian (2007) propose that the ... • 13.2k 13 votes 5 answers 6k views ### How to obtain true probabilities from Black-Scholes? How to obtain true probabilities from Black-Scholes option pricing equation? Suppose, that we know risk adjusted discount rate for the underlying asset (the drift term in the physical measure) and ... • 133 5 votes 2 answers 13k views ### How can I calculate the strike price or implied volatility from a given delta? I have calculated the implied volatility for all strikes of a certain product (options on futures) and approximated the ATM volatility. My question is how can I figure out the implied volatility for a ... • 357 4 votes 2 answers 399 views ### Option Valuation Can Black-Scholes option values be derived via the Capital Asset Pricing Model, without resort to the use of a risk-free portfolio being created from the option and a Delta determined quantity of the ... 2 votes 1 answer 1k views ### Carr-Madan european contingent claim payoff decomposition formula - application Looking for some clarification to the values of the parameters used in the Carr-Madan payoff decomposition formula.$$f(S_T)=f(\kappa) + f'(\kappa) (S_T - \kappa) + \int_0^{\kappa} f''(K) (K-S_T)^+ ...
Let imagine we have an option from EUR to USD priced in EUR, therefore the payoff for a call is: $$\frac{(S - K)^{+}}{S} = K (1/K - 1/S)^{+}$$ This is basically the payoff of a price of a put on 1/S ...