# Questions tagged [european-options]

An option that can be exercised only at expiration.

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### Vega of forward volatility

Imagine I have two European-style options that are the same except for their times to expiry: $T_1 \lt T_2$. And each option has its own vega $\mathcal{V}_1$ and $\mathcal{V}_2$. My question is: what ...
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### Quantlib Heston MC Discrepancy between methods

I am a newbie at Quantlib (not finance) and am trying to price with the Heston model. I have implemented two different ways to verify the correctness of the Heston path generation to use in a custom ...
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### Why does the lower arbitrage boundary of a European call on stock rise with time if F > S but fall if F < S?

I am reading "Option Volatility & Pricing", 2nd edition, by S. Natenberg. On page 297, he explains the lower arbitrage boundary of European options. I don't understand the logic for what ...
223 views

### Monte Carlo simulations with extremely high volatility

I am using monte Carlo simulations to price a forex option. This is a standard model and works very well with less than 1 % error from black scholes price for 10000 simulations. But, as I increase ...
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### Upper Bound on European/American Call Option (Hull)

I recently began reading Hull's derivatives textbook, and found a line that he didn't expand on much. Let $c$ be the price of a European call, $C$ be the price of an American call, and $S_0$ be the ...
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### Potential arbitrage opportunity or fallacy?

Suppose we have two European options with the same expiration: a call priced at $c$ with strike price $K_1$ and a put priced at $p$ with $K_2 (>K_1)$. Further, suppose the zero-points of the two ...
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### Understanding basic options arbitrage in Hull

I’m reading Hull’s book, Options, Futures and Other Derivatives. In Chapter 11 he discusses put-call parity and the arbitrage opportunities that can result from its violation. I’m having a basic issue,...
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### Implied Vol under CEV model

Consider the following steps: Suppose the underlying equity follows a CEV model $dS_t = rS_t dt + \sigma S^{0.5} dW_t$. Use the above CEV model to simulate Monte Carlo paths and price a large set (...
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### How do linear wings reconcile with volatility frowns

I was recently looking at a paper that brought up that under certain market conditions the risk neutral density can exhibit thin tails, yielding a volatility frown as opposed to the more usual ...
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### Volatility Surface Modelling in Python

For my master thesis, I try to create a Volatility Surface for S&P500 Index options. Every time I run my code, the surface I get is full of spikes. I'm just not sure if these are outliers which ...
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