Questions tagged [european-options]

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13 views

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. ...
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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 ...
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1answer
94 views

Why does my equity option pricing model not converge? [closed]

I have written a python implementation of the Equity option pricing model from: advanced quantitative finance with C++ by Alonso Pena The model I am implementing takes the form: $dS = rSdt + \sigma * ...
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42 views

HNGARCHFIT in R (No standard deviations or P values printed)

When I estimate an HN-GARCH model using the hngarchfit() from the fOptions package in R, only the coefficient estimates are printed. There are no standard deviations or P-values printed. Does anyone ...
2
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1answer
63 views

European call option lower bound derivation by Black-Scholes formula [closed]

Derive the lower bound of european call options: $$C(S, t)\geq[S-e^{-r(T-t)}K]^+$$ I know how to derive it using put-call parity, but is there any way to derive from Black-Scholes formula?
2
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1answer
64 views

How to approximate a delta using monte carlo methods and finite differences via Higham's book?

I'm currently taking a Mathematical Finance module at University and one of the recommended texts is “An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation” by D.J. ...
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1answer
57 views

Reason why a European binary call should be worth half of its American counterpart when driftless and out-of-the-money

Exercise 11 of chapter 8 of Mark Joshi's "The concepts and practice of mathematical finance", asks to compare prices of an American and a European digital (binary) calls when out-of-the-...
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50 views

Solution of the following PDE using European put option

I'm reading some articles about PDE and I found the following PDE, with $q_1,A >0$: $g_t(t,y)+ \beta^2yg_y(t,y)+\frac{1}{2}\beta^2y^2g_{yy}(t,y)-q_1 g(t,y)=0 \quad (t,y) \in [0,T), \times (0,+\...
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0answers
46 views

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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74 views

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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37 views

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 ...
2
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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 ...
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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 ...
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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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0answers
95 views

Is this the PnL you would expect to see for a hedged call option portfolio? [closed]

You are a market maker. Charging no commission, your only aim is to remain market (delta) neutral. Therefore you construct a portfolio of the form: $$\Pi = -C - w_{1} B + w_{2} S$$ where $B = K \cdot ...
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3answers
107 views

Intepreting European call option when expiration approaches to infinity

Assume that dividend = 0, then the price of call option is $$ C = S\cdot P_{s}[S(T) > K] - e^{-rT}K\cdot P_F[S(T) > K] = SN(d_1)-e^{-rT}KN(d_2) $$ where $P_s[S(T) > K]$ = Probability of ITM ...
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0answers
32 views

Intraday “Time to expiration” for Black-Scholes on the expiration day

In Black-Scholes, T is the % of year, how do we calculate T intraday on the expiration day? Does the expiration happen at the exact moment of that trading session? For example, for SPXW options that ...
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1answer
141 views

How to price an European put option using binomial model with dividend yield?

The initial stock price (S0) is 45, the stock volatility is 0.20 (20% per annum), and the risk-free rate is 0.02 (2% per annum). Consider a European put option whose strike price is equal to 30, with ...
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0answers
61 views

Option where option writer determines type of option to give to holder

I am currently looking at an exotic option that allows the holder, at some time $\tau$, to receive either a call or put — the choice of which is decided by the option writer — of which both have the ...
1
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1answer
174 views

Hull's book - Futures option's rho

In Hull's book (9th edition), on page 420, in table 19.6, it says rho of a European call on an asset with yield $q$ is $$KTe^{-rT}N(d_2)$$ Below it says we can compute greeks of European options on ...
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1answer
61 views

Maximal increase payoff

I am interested in the following problem. We have a Multi-Step Binomial Model with discrete time $T=1,\dots,n$. We also assume that the stock $S_t$ is a martingale and there is a risk-free bond with $...
1
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1answer
79 views

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 ...
2
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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, ...
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23 views

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; ...
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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 ...
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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". ...
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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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0answers
44 views

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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0answers
49 views

Put-call parity under a regime-switching model

I need some help. I'm given $J$ different regimes, each one characterized by its own parameters $(r_i, \delta_i,\sigma_i,...)$ with $i\in \mathcal{J}= \{1,2,...,J\}$ ($r$ = risk-free interest rate, $...
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2answers
165 views

Reason to hedge a European call option

Assume I write a call option on one share of the stock that I have. After selling the option I have an obligation to sell one share of the stock at some future time. I already have the stock, why ...
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2answers
153 views

Why are there so many S&P 500 call options selling with strike @1000?

I am analysing option-implied RNDs and risk preferences for my masters thesis, so forgive me if I sound like a beginner in derivatives. I use WRDS to download my historic options data. I am looking at ...
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2answers
398 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 ...
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1answer
71 views

Can a down-and-out barrier call option be priced using the Black & Scholes formula or should it be approximated?

I am trying to price of a Down-and-Out Barrier call option with leverage. When the price of the underlying asset hits a certain barrier (B), the option becomes worthless. The issuer of these options ...
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2answers
86 views

Why are these deep in-the-money FLEX options seemingly bought at a discount?

98% of the initial reference value is .98 x 267.88 dollars, which equals 262.52 dollars. However, the market value of each call contract they purchase is 247.42 dollars. How are they purchasing these ...
2
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1answer
106 views

Free or cheap data source for the current European Options prices?

Is there a free or cheap (<15$/month) data source for the current (not historical) for European Options? Something like Yahoo Finance option page, with option chain contract prices. It's ok if it's ...
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1answer
65 views

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^{-\...
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1answer
288 views

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) ...
3
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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 ...
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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 ...
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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 ...
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2answers
99 views

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 ...
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0answers
46 views

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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
112 views

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 ...
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2answers
306 views

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....
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1answer
63 views

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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0answers
57 views

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(...