Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [european-options]

The tag has no usage guidance.

1
vote
0answers
17 views

Historical options data for FX/FI

I know that my question is quite large and that quite a lot of questions already deal with the options data. However most of questions deal with options on American equity markets. Could you ...
4
votes
0answers
33 views

Stochastic Long-Run Mean Instantaneous Variance in Heston Model (and extensions)?

I'm working on my dissertation in Financial Economics, focusing on the topic of Stochastic Volatility Jump Diffusion models; and I'm playing around with some ideas for model extensions. In particular, ...
0
votes
2answers
129 views

What is the second derivative with respect to price of a put option? [closed]

What is the reasoning/meaning behind the second derivative of a put option
0
votes
2answers
83 views

Is American option price lower than European option price?

I used to think under the same condition, the American option is always more expensive than the European option, because American option can be exercised at any time (has more rights than European ...
2
votes
1answer
108 views

Arbitrage when risk-free portfolio earns less than riskless portfolio

I'm currently reading Paul Wilmott's excellent book on option pricing. Near the beginning, he constructs a risk-free portfolio using an option, and a short on the underlying to hedge the risk. I'm ...
3
votes
2answers
96 views

Conceptual explanation of the relationship between gamma and vega plotted against delta for a European call option

I recently plotted Gamma and Vega against Delta for a European call option and found that the graphs look very similar. This makes sense to me mathematically since the two formulas are pretty much the ...
1
vote
1answer
47 views

European put price when stock price is 0 before maturity

According this answer, https://quant.stackexchange.com/a/39298/29108, the European put price (with maturity $T$) at time $t$ for a stock whose current price is $0$ should be the strike $K$ discounted ...
4
votes
1answer
98 views

How do I compute Value at Risk of a European call option?

Consider a European call option on a non-dividend paying stock, where the option has strike K = 100 and expiry T = 0.25, i.e. the option expires 3 months from now. The option is on a single share. The ...
0
votes
0answers
42 views

If the value of a call option is not dependent on the drift of the stock, why does a higher stock price mean a higher call option price [duplicate]

I have read that the price of an option is not affected by the drift of the stock since the drift term doesn't appear in the Black Scholes PDE. I become confused because to me, this implies that the ...
0
votes
1answer
60 views

Why does a higher stock value imply a higher call option value [closed]

This may seem like a very dumb question, but if the underlying stock price is greater, then why should a call option be worth more. My reasoning is that, if the option price is not affected by the ...
3
votes
1answer
152 views

Dependency of an option price on time till expiry

I am trying to seek satisfaction when it comes to understanding why the price of an option is dependent on the time until expiry. I have read that the longer till expiration, the more time available ...
2
votes
1answer
85 views

European put options

Why is it that for European Puts on Non-Dividend-Paying Stocks, the lower-bound for price is $$p=Ke^{-rT}-S_0?$$
3
votes
2answers
204 views

What is the Brownian motion in the model for the return of a stock price trying to capture?

I have read that in the derivation of the Black-Scholes PDE, we assume that the return of a stock $S$ is given by $$\frac{dS}{S}=\mu dt+\sigma dB$$ where $\mu$ is the average growth of $S$, $\sigma$ ...
1
vote
1answer
36 views

Iron condor with positive vega

I am backtesting this Iron Condor before earnings. In the position summary Vega (Mid Quote) is -3.04\$ but in the chart below (IV vs Profit $) it's clearly shown that a decrease in volatility will ...
3
votes
1answer
108 views

Pricing a call option with pay-off function max{$S_T - S_{T/2}, 0$}

Pricing a call option with payoff function $C=\max\{S_T - S_{T/2}, 0\}$, where $S_T$ is geometric brownian motion. I appreciate any help! Please close this question if this is a duplicated question. ...
0
votes
1answer
98 views

Basic Replication of European Call Option

I am looking at the very basics of replicating an option with a portfolio of risky and risk free assets. As such we can define a portfolio of $x$ no. of shares, $y$ bonds & $z$ options at time $(T)...
1
vote
1answer
97 views

Why futures pricing not calculated like options?

I have read about futures and options ( from online resources ). I only have the basic understanding,not math heavy ( for eg. for Black Scholes I know only the intuitive idea from the khan academy ...
1
vote
2answers
173 views

Why do we need to calibrate vega?

I was going through some paid video on options. The tutor in the video asked the following question: Person $A$ has the following portfolio at the start of April Portfolio of options with vega $20,...
3
votes
1answer
204 views

Option Strategy: Python Implementation Advice

I've been tasked to create and backtest an option strategy. The strategy, in vague terms, is to essentially write call options on securities in a universe, i.e., selling insurance. I have an idea of ...
1
vote
3answers
245 views

From Butterfly Price to Probability of $S_T$ Falling within a Range

If a butterfly in the limit represents a probability (by the Breeden-Litzenberger result), what can be said about the relative likelihood of a random variable $S_0$ from the price of a vanilla-option ...
2
votes
1answer
76 views

Perpetual Put vs European Put

I am looking at a perpetual put option where the strike price is initially the stock price $K(0)=S(0)$ (i.e. at the money), but the strike price grows at the constant risk-free rate $r$ [i.e. $K(t)=S(...
1
vote
0answers
90 views

Best Way of Interpreting Black-Scholes Formula [duplicate]

I'm curious to know the best interpretation of the Black-Scholes formula for a European equity call option: $$C(S,t)=S_tN(d_1)-Ke^{-r(T-t)}N(d_2),$$ where $d_1=\frac{1}{\sigma\sqrt{T-t}}\big[\ln(\...
2
votes
0answers
51 views

Forward spot calculation for a dividend paying no-short sell ETF

I am trying to fit an implied volatility curve for options on the SSE 50 etf that has no borrow (no short selling allowed) and pays a single annual dividend. I originally thought I could use the ...
1
vote
1answer
127 views

Upper bound option price in volatility dimension

All, I have a theoretical question about the value of an option when spot price goes to infinity as a function of volatility going to infinity. I know that for a call option: The option value ...
2
votes
0answers
25 views

Use of second similar European Option as control variate to simulate a European option

I understand the idea and math behind the concept of control variate for the sake of variance reduction, but I struggle to apply it to option pricing. I need to simulate an European option of a stock ...
7
votes
1answer
553 views

Option pricing and mean reversion

In different books one can find a formula for option pricing when we assume that $\ln(S)$ follows a mean reversion process $$ dS_t/S_t=\kappa(\theta-\ln(S_t))dt+\sigma dZ$$ If we calculate an ...
1
vote
2answers
88 views

Calculating implied volatility from moneyness/volatility values for date

For an option expiring at a particular date I have Moneyness 0.4,0.7,0.85,0.95,1,1.05,1.15,1.3,2.5 Vol 0.105,0.075,0.045,0.045,0.202,0.045,0.045,0.075,0.085 ...
0
votes
0answers
125 views

calculating implied volatility of Asian Option

I am new to the site. I saw another similar question but I can't comment on it because of low rep. I wanted to know how the volatility of an Asian is calculated. I was thinking that a weighted ...
3
votes
0answers
79 views

Can the vega of ITM call-options be negative when the distribution of the underlyings returns is negatively skewed?

While calculating european call option prices, using the variance-gamma model formula provided by Madan, Carr & Chang (1998), I noticed that, holding all other things constant, the value of an ITM ...
1
vote
1answer
104 views

Dividend yield on ASX 200 (XJO) index options

I'm trying to understand how to calculate the price and Greeks of XJO options. XJO options are European, the underlying is an index and they don't pay a dividend. However the underlying drops when ...
1
vote
0answers
66 views

Pricing and hedging OTC vanilla options

Most OTC option textbooks are about exotic options. I'm curious how sell-side price and hedge OTC vanilla options e.g. European option. What models do they use? How to forecast volatility (using GARCH?...
-1
votes
0answers
35 views

Explicit finite difference solution of the diffusion equation

Does anyone know where I could find a numerical example of how the explicit/implicit finite difference methods can be used to evaluate the value of an option for both European and American styles. I ...
0
votes
0answers
158 views

Arbitrage Strategy Long American Call and Short European Call

We know for the fact that the holder of an American call option has all the same rights as the holder of a European call option and more. This also results in American call option always worth at ...
2
votes
1answer
56 views

How to handle bid-offer spread causing negative estimations of risk-neutral densities from option prices?

I have attempted to estimate the risk-neutral probability density, from CBOE options prices on S&P500 from 2010 to 2016, using the following approximation from Hull (2018). For call options on a ...
5
votes
0answers
89 views

Pricing and hedging of vanilla options based on non-tradable underlying

Consider a non-tradable stock index $S$ which satisfies: $dS_t=\mu S_tdt+\sigma S_tdW_t$ and a risk-free asset $B$. I want to price an European Call option with the payoff $C_T=max(S_T-K,0)$. The ...
2
votes
1answer
232 views

European option Vega with respect to expiry and implied volatility

I was told that the Vega of an European option always increases when its time to expiry increases (all else equal). I found this confusing and potentially wrong, but there doesn't seem to be relevant ...
0
votes
1answer
291 views

Am Call = Euro Call if r is non-negative and Am Put = Euro Put if r is negative

It can be proven that under non-negative interest rates, it is never optimal to exercise an American call option, such that: We know, if R >= 0, the current price C of a Europen (and American) call ...
1
vote
1answer
280 views

Valuation of Bermudan option as maximum of relevant European options

Assume I need to price a Bermudan option which can be exercised at following dates: $t_1$, $t_2$, ..., $t_n$. I think that the price of such an option will be maximum of the prices of European options ...
2
votes
1answer
62 views

Pricing Secured Barrier Call 2

EDIT: OK, I understand the reasoning for the initial answer now; however, I don't understand why we would need the digital call with a strike of 33 in this question. Is it just there to serve as a red ...
2
votes
0answers
87 views

Second order convergence for the Leisen-Reimer tree

I have a question about this paper "Achieving higher order convergence for the prices of European options in binomial trees" by Mark Joshi, (Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=...
0
votes
1answer
85 views

Quoting options with reference price and delta

I always thought equity options where quoted with implied volatility, the price being given by the Black-Scholes price of the option with volatility equal to the implied volatlity. But apparently ...
1
vote
0answers
29 views

Spectral Analysis for European Put Options

I am trying to implement the spectral analysis on European Put Options. My code is designed to change the number of nodes(basis functions) accordingly, but the boundary condition and thus the range of ...
1
vote
0answers
29 views

Option style with grant date

The following option exercise style is somewhere between American and European: There is a fixed grant date $N_1$ at which you determine at which date $N_2>N_1$ the option will be exercised. So ...
0
votes
1answer
124 views

How to show arbitrage when a European option price is greater than the no-arbitrage price?

My example is: Current price = 20, If it goes up it'll be worth 22, if it goes down it will be worth 18 risk free rate: 12%, time = 3 months Strike = 21 call option is worth 0.633 I know that if the ...
0
votes
1answer
100 views

ITM call delta when T increases

for an expiring European in-the-money (ITM) call (delta = 0.9), if $T$ increases from 1 to 30, what should delta be now? Let's say $K = 100$, $S_0 = 105$, $\sigma = 10%$. Intuitively I think the ...
2
votes
2answers
2k views

A simple question: Cost of delta hedging when a call option is sold

Consider a vanilla European call option C, with underlying asset S, strike price K and time to maturity T. Assume that S follows a geometric Brownian motion with mean growth rate of μ and volatility σ....
-1
votes
1answer
193 views

Why does option pricing not depend on probabilities in a binomial tree style valuation

I am new into learning option pricing and read that option pricing using binomial valuation does not depend on probabilities (real or risk neutral). Example: A 1 period binomial tree with $u = 1/d = ...
1
vote
0answers
89 views

Binomial Option Pricing - Hedging

I'm working on a project which is requiring me to test Binomial option pricing on real data. So far I have just been working with test data and my option pricing method works fine. The issue I'm ...
0
votes
1answer
141 views

How to use daily and hourly prices in same option model?

An option can be exercised hourly but depends on two prices - one is available daily and hourly, the other one only daily. How can I write an option model that uses a quadrinomial lattice with both ...
2
votes
1answer
123 views

Is there any useful links for option pricing (american + asian + european) using R

I'm trying to evaluate option pricing mainly american, asian and european options in order to get a plot to measure option valuation in time. Is there any useful references to do that using R ?