# Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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### What is the minimum price of an option, given no information about Greeks? [closed]

I was asked this interview questions for an analyst level structuring role and it has been bothering me since I can't figure it out: Assuming the price of an equity is 100, what is the minimum price ...
213 views

### Given $\mathbb{E}[X]$, $\mathbb{E}[\max(0,X)]$, and $\mathbb{E}[\min(0,X)]$, what is $\mathbb{E}[f(X)]$

Let $X$ be any random variable with any distribution. Given that we know $\mathbb{E}[X]$, $\mathbb{E}[\max(0,X)]$, and $\mathbb{E}[\min(0,X)]$, can you write a formula for $\mathbb{E}[f(X)]$ where $f$ ...
1 vote
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### I can’t understand why the premium of two butterflies with same strike but different broadness are approximately the same

Consider the following premiums of calls option with different strikes. C90 = 57.35 C95 = 52.55 C100 = 47.3 C105 = 42.9 C110 = 38.25 In this case, the butterfly 90-100-110 cost 1 and the 95-100-105 ...
119 views

### How do you explain consistently making money with discrete hedging a call option?

In a backtest I did, I'm selling a call option and buying a delta amount of the underlying (calculated using implied vol). Now I know in the limit case of continuous hedging I end up paying a PnL ...
594 views

### Is Local Volatility a function of the Strike or the Underlying price?

Long story cut short: I am asking why the Local Volatility function can be thought of as a function of the underlying, when in fact it appears to be a function of the strike. Additionally, I wonder ...
147 views

### Pricing options in underlying problem

Let us look at options, which are cash settled, but instead of receiving cash, you receive the proportion from underlying asset with the same value as cash. Moreover, you can pay for these options in ...
186 views

### How do you handle non integer time intervals in Quantlib for options pricing (ie intraday pricing)

I'm using QuantLib (python version) for options pricing, and am trying to figure out how to handle non integer dates. If you try and price an option at 9:30 AM and at 4 PM, you should get different ...
1 vote
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### Exotic options with lookback features [closed]

I am trying to value an american call option with a lookback feature. So the holder can choose to exercise either based on a fixed strike (K) or a floating strike equal to 10-day moving average (MA). ...
620 views

### Mid-curve swaption pricing - how to get the spread vol?

I believe I understand the following (from the accepted answer to the Quantitative Finance question called "volatility of a mid curve option"): A swaption in which the underlying swap ...
204 views

### Implied volatility skew decay over expiry

I seem to remember the implied volatility skew of European options decreases as the expiry increases. It is true for the Heston model under some approximation. What are the good references that prove ...
225 views

### Probability density from COS method too sensitive to truncation range

I have a long-standing confusion around the truncation range of the COS method proposed by Fang and Oosterlee because I find that the results are highly volatile given the different truncation ranges. ...
1 vote
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### VIX options: vertical mark price vs. term structure

Does anyone have any hypothesis why, for options on a future series, vertical spreads priced at half the strike difference should exhibit the same strike across all expirations, regardless of term ...
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### How do I proceed with pricing after calculating local vol volatilities?

What are the next steps for pricing under the local volatility formula? It feels like I'm missing the trick (as I only see the numerical methods used to obtain prices after calculating local vol). I.e....
426 views

### FX Option Vol Quotes (Days or Days+Time to Expiry)

I understand FX Options are often quoted via ATM, RR, BF for 10/25 deltas. There are many resources that outline how to convert those quotes back into absolute strike space (using spot delta or ...
220 views

### Very close local volatility and implied volatility using Dupire's equation

I used Dupire's equation to calculate the local volatility as in https://www.frouah.com/finance%20notes/Dupire%20Local%20Volatility.pdf and Numerical example of how to calculate local vol surface from ...
337 views

### Black and scholes option pricing

I have to solve the following problem in the Black and scholes model: find the price at anty $t\in[0,T)$ for an option whose payoff at the maturity is: \begin{equation} 0 \ \ \ \text{if} \ S_T<K_1\\...
119 views

### In the derivation of the Black-Scholes PDE, using delta hedging, how is this linked to the risk neutral valuation? [closed]

I was reading this paper: http://www.columbia.edu/~mh2078/FoundationsFE/BlackScholes.pdf I don't understand the paragraph here: "The most interesting feature of the Black-Scholes PDE (8) is that ...
1 vote
136 views

### Why should delta-neutral backspread always result in credit?

Natenberg mentions in chapter titled "Volatility Spreads" : under the assumptions of a traditional theoretical pricing model, a delta-neutral ratio spread where more options are purchased ...
114 views

### Any innovations in mathematical processes behind option pricing models?

I am working on my thesis about option pricing models beyond classical Black-Scholes Model by looking for some recent innovations on mathematical processes behind the pricing structures. By that I ...
1 vote
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1 vote
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### What is the optimal time for exercising American call and put option?

A 9 month American option (underlying) is known to pay dividend of USD 1 and USD 0.75 at the end of the ...