# 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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18 views

### Hindsight overhedge for pricing path dependent options

I understand how to use the longstaff schwartz method in Monte Carlo to compute the continuation value of path dependent options but someone recently mentioned another technique called "Hindsight ...
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### Do Perpetual American Options have closed form functions to compute the Greeks?

I was wondering if there were analytical formulas to compute delta or gamma for perpetual American options?
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### What equation will convert implied yield volatility to implied price volatility?

I am trying to figure out how to turn implied yield volatility of a short-term interest rate into implied price volatility. Is there an equation to do this? I have come across the equation for a ...
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### Varswap replication product

I would like to ask about a product that some Flow desks sell : Varswap replication strategies. I know that it consists of weighted basket of calls and puts , however I would like to know how does it ...
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Suppose I am long spread option with underlying : rate A - rate B. The vega on the option would be positive. But if I want to compute the option vega with respect to individual rates, can I use the ...
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### What's the formula to compute the divided difference approximation for the third order greeks?

I can't seem to find the quotient required to approximate the third order greeks Speed, Zomma, Color and Ultima
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### Black-Scholes vs Blacks model. Which one to use with SABR?

Say I want to compute a call price for a given set of SABR parameters. I use Hagans approximation and compute $\sigma_B$. The rate is not zero. Should I then compute the option price using Blacks ...
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### What is the best book to learn about local vs. stochastic volatility, modelling and pricing of Exotics?

I am starting to delve into the world of Exotics and I am trying to find a rigorous yet understandable book that covers both mathematically and qualitatively (especially mathematically) the following ...
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### 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 \begin{equation} C(K) = S_0 \Pi_1 - ...
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### Really simple question regarding options. (Amateur level)

I'm just starting to educate myself on trading and financial instruments and I have what to me seems like a somewhat stupid question but I'd like to pose it nontheless. If I have an option to sell ...
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### Generalisation of calendar arbitrage condition to options on futures

This question has discussed the condition on which calendar arbitrage opportunities arise for European call options on a stock. Do similar criteria exist for European options on futures? The most ...
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### Will the Delta of an Option always be the same irrespective of the underlying stock price?

Suppose, under the Black Scholes model we keep all the parameters the same except that we vary the asset price. Will the Delta of the option always remain the same?
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### Simulating assets of different currencies

I have a situation as follows: One year call option on a Euro stock with a Euro denominated strike. Knock in feature as follows - The option can only pay out if the growth in the Euro stock over ...
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One can trade vol swap to get exposure of the volatility of the underlying security in a 'clean' way. On the other hand, we know that vol swap, theoretically can be replicated by a dynamic position of ...
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### FX Options Greeks: Is there a meaning in converting the sensitivities values in different currencies?

Suppose you have a Call on JPY, domestic currency is USD The price will be in USD Let's say delta = 0.93 Does it make sense for any reporting reasons to convert this value into JPY ? What is even the ...
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### Black Scholes Replication If Underlying Does Not Move?

Let's say you are long a call and want to replicate that call buy being short underlying and long bonds. If the underlying moves up in the next period but not enough to cover theta, the option ...
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### How can the implied volatility be calculated?

We all know if you back out of the B.S. option pricing model you can solve for what the option is "implying" about the underlyings volatility. Is there a simple, closed form, formula deriving Implied ...
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### Implied volatility of Treasury options

For practitioners, does the concept of implied volatility also apply to (European) Treasury Options (whose underlying is Treasury Futures contracts)? For the standard individual stock vanilla ...
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### Prove the following Call and Put relationship: [duplicate]

I need to prove that $$c(S,X,T)=\frac{X}{F}p(S,\frac{F^2}{X},T)$$ where $$F=Se^{(r-q)(T-t)}$$ I am having trouble proving this relationship. Is this relationship even possible? If so, can someone ...
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### Does high levels of vol-of-vol parameter in SABR lead to Arbitrage? (Something seems wrong with Hagans formula)

Main question: Do we need to restrict the vol-of-vol parameter in SABR further than $\text{vol-of-vol}>0$ and how do we determine the interval of vol-vol which the model is arbitragefree? ...
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### Any good book recommendations for learning The Greeks?

I am interested in getting a good "feel" or intuition for the BSM Greeks. Specifically, i'm looking for a book which is light on the math (but not too light) and easy to read and understand. I am also ...
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### What is the cause of a “broken” volatility surface?

I am currently working on a project for which I need the implied volatility surfaces, to estimate the value of plain-vanilla European options with different strikes (cannot be observed directly in the ...
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### Equivalence of Put Pricing Formulas

I have to show that: \begin{equation} P_{t,T}(K)=e^{-r(T-t)} \int_0^{\infty}\left(K-S\right)^+ q_T^S(S)dS \end{equation} is equivalent to: \begin{equation} P_{t,T}(K)=e^{-r(T-t)}\int_{-\infty}^{...
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### Measuring implied move priced into an event

It's well known that options price in an expected move in the underlying going into events, such as earnings announcements. I currently measure this implied move by computing the forward variance ...
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### Computing option price with rates only

Hi I am learning about options and came across this example: The spot FX rate AUD/USD is 0.6868, the 6 month ATM implied volatility for AUD/USD is 7.7% p.a., for the 6 month USD deposit rate is 2.28% ...
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### Pricing barrier option under Levy process: Biased estimate?

I want to price a down and out call, barrier option, with the underlying asset following a Levy process. I am interest on the Kou double exponential model or the NIG process, to capture asymmetric ...
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### Is the implied volatility surface relative or stationary?

Do different strike values of options attain their volatility value dependent on their % distance from the ATM price continuously, or is the volatility surface stationary during a single day?
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### Black's Approximation - Discrete dividend for Put Options

I am currently trying to price and option chain for dividend paying stocks (american style exercise). I am able to calculate the Net Present Value (NPV) of dividends until maturity and then apply ...
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### Why can't we create a “magic” basket of options to sell for no-arbitrage pricing in SVJ model?

I am learning how to price SVJ options and am reading some stuff on no-arbitrage pricing for SVJ model using the typical approach you would use (like in BSM option pricing) of creating a risk free ...
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### How to interpret the (expected) exposure and CVA of an option or a single share

I have a quick (hopefully simple) question regarding the interpretation of the expected exposure of a call option and a single share. I've done some computations on the formula for the expected ...
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### One-day Binary Event Implied Moves

What is the convention for pricing the expected 1-day move of a binary event based off of the implied volatility of the nearest series which contains that event? How do you distinguish between the ...
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### Pricing structured products (Mortgage Backed Securities) [closed]

What would someone have to do to be able to price a structured product like Mortgage/Asset Backed Securities?