# Questions tagged [european-options]

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### Conceptual doubt on when to use cost discounting [closed]

In this question I have used put-call parity twice to get the discounting factor for time period 0 to t (which I feel is of no use for this question). Also I found the initial payoff and final payoff. ...
1answer
80 views

### Why is implied volatility often higher for OTM/ITM european call options than ATM? [closed]

I am working on some Black-Scholes stuff and currently investigating implied volatility (IV). I understand that the typical volatility smile can be viewed as a criticism of the assumption about ...
1answer
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### Price of european call option for different strike prices

Consider two european put options with strike prices $K, J$ with $K<J$ and maturity $T$. Then the no arbitrage assumption implies $P_{K}(0)<P_J(0)$, where $P_K(0)$ denotes the price of the put ...
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### Forward Index Level in VIX calculation

The VIX white paper (https://cdn.cboe.com/resources/vix/vixwhite.pdf) step #1 (page 6) says the the Forward Index Price is calculated as: F = Strike Price + e^RT x (Call Price - Put Price). Why doesn'...
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### Calculation Option Greeks per day using Quantlib

I'm trying to calculate option greeks and impVol for a series of European index options (they are in a DataFrame) using QuantLib. Is there a way to get the Greeks and impVol on a daily basis? Thank ...
1answer
114 views

### Intrinsic Value of European Options [closed]

I have a question regarding the intrinsic value of an European option. I use the following notations: $S_t$ price of the non dividend paying stock at time $t<T$, $T$ is the maturity, $r$ risk-free ...
2answers
85 views

### Prove the Euro call option value has positive relationship with the risk-free rate under discrete time model (Binomial tree model)

Could anyone show me how to prove that the European call option value has a positive relationship with the risk-free rate in a two-step binomial model with strike price K and different risk neutral ...
1answer
112 views

### Barrier Reverse Convertible

I am a finance student and during my free time I try to understand more financial products. Today I have found a term sheet for a specific type of barrier reverse convertible but I couldn't understand ...
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1answer
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### Investigating how rational price of European call option changes [closed]

Let S(0) = 100 be the initial price of the risky asset. Consider a European call option with exercise price K and expiry time T = 1 (year). Consider several binomial models and investigate how does ...
1answer
77 views

### European call option on constant volatility or drawn from a volatility distribution

Which is more expensive: A European call option on constant volatility of 30% or or drawn from a random distribution of mean 30%? The answer in A Practical Guide To Quantitative Finance Interviews, ...
0answers
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### Seed Values guaranteed convergence of Implied Volatility Calculation

Looking for good seed values for Newton Raphson to guarantee convergence of implied volatility calculation for a few models, all of which are for equities that have divs. 1) Bjerksund-Stensland 2002; ...
2answers
258 views

### How do I prove that a certain price is price of European option in Black-Scholes framework

I want to show whether the following price at t is of a european option in Black-Scholes Framework. $$S_tlog_e (S_t^3)$$ Is it just trying to substitute the function (and partial derivates) in the ...
1answer
32 views

### is price of multiple option strategy linear under expectation? [closed]

I wonder if someone can confirm (or refute) that the expected payoff of several option (in a strategy such as a spread, condor, etc) behaves as "expection of a sum is sum of expectations". ...
1answer
60 views

### Single-period market with probability space [closed]

Let $C^E$, $P^E$, $C^A$, and $P^A$ denote prices of a European call option, a European put option, an American call option and an American put option, respectively. All of them with expiry time $T$ ...
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### Issue in Understanding the Boundary Conditions for European Call Option in Implicit Finite Difference Method

I have a working Python code which prices European call option in Implicit Finite Difference setting. However, I am unable to understand the Boundary Conditions implemented on the coefficient matrix ...
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### FX pricing replication

Pay in currency : cur The FX is : $FX^{cur_2/cur_1}$ European options on the FX (and itself) are quoted in currency cur 1. I'm looking for the price of \begin{equation*} \mathbb{E}^{Q} \left[ e^{-\...
1answer
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### How to best predict option prices using Brownian motion and compare it to the Black and Scholes model?

I am trying to use Brownian motion to predict option prices and compare the outcomes to Black and Scholes. For this purpose, I would like to calculate the average returns (mu) and volatility (sigma) ...
1answer
373 views

### Converting an American option to European option [closed]

I wonder if there are any websites/resources/sample codes/papers on how to convert the American options to European options (when all else are equal). i.e. if given same underlying asset, same ...
2answers
115 views

### Failing to replicate Wilmott's results for binomial option pricing

I am working through Paul Wilmott introduces Quantitative Finance, 2nd ed. I am failing to reproduce one of his numerical examples and I would like to understand why. I chapter 3, Wilmott introduces ...
1answer
195 views

### Under what conditions will both European and American put options worth the same?

It is well-known that on a non-dividend paying stock, it is suboptimal to exercise an American call option earlier. In other words, both European and American call options on the same non-dividend ...
2answers
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### How are option values in real life calculated without volatility?

Implied volatility is the volatility that when inputted in the Black-Scholes model, it returns the theoretical market price of a European option value. I understand that implied volatility is not ...
0answers
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### Black-Scholes pricing of european call option

I am really confused on the usage of the greeks and the Black-Scholes model for option pricing. To gain some more understanding I am attempting to see if I can price a european call option under the ...
1answer
101 views

### How to evaluate embedded floor option in inflation linked bonds if interbank inflation floor instruments cannot be used or do not exist

Suppose we consider simple case that only par is protected against base price index, so it is with zero coupon floor feature. How do we value this option given that there is no inflation floor ...
0answers
53 views

### What is a lookback rate put option

I've come across an option called a look-back rate put option. However, the source I got this from did not say what this is. I understand what a look-back put option is, but the rate bit is throwing ...
0answers
29 views

### No unique no-arbitrage price when the stock price can remain unchanged

In a 1-period binomial model, with initial stock price 100, if the stock price is either 50,100, or 150 after 1 period then how can I show there is no longer a unique no-arbitrage price for a European ...
1answer
105 views

### Butterfly spread calls and puts

I am trying to understand the butterfly spread. My book (ASM Study Manual for SOA Investment & Financial Markets (IFM) Exam) says one of the ways to write it is: Long put, strike $=K-c$ Short ...
1answer
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### Arbitrage between American and European put options on the same underlying asset

Suppose there exist both American-style and European-style put options on the same underlying asset, at the same strike price, and with the same expiry date. Suppose the European put is selling below ...
2answers
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### Python Monte-Carlo Convergence

Edited to include VBA code for comparison Also, we know the analytical value of the simple Call option, which is 8.021, towards which the Monte-Carlo should converge, which makes the comparison easier....
1answer
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### Are there values of the strike price for which an American put and European put have the same no-arbitrage price?

Assuming the options do not pay dividends, is there a strike price that satisfies this?
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### Fourier transform Carr-Madan method on an arbitrar initial $S_0$ values

As mentioned in Carr-Madan's paper, here, the European call option is: $$C_T(k)=\frac{e^{\alpha k}}{\pi}\int_0^\infty\mathcal{Re}\left(e^{-iuk}\psi(u)\right)du$$ where  \psi(u)=e^{-rT}\frac{\phi_T(...