Questions tagged [european-options]

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32 views

Where can I find the formulas to compute the Greeks for European Call and Put Options Assuming no annual dividend yield?

Every formula I come across involves a $q$ (the annual dividend yield). Where Can I find the formulas to compute the greeks assuming no dividends?
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48 views

What is the reason that an American option has a lower volatility than an European counterpart?

I was researching some plain vanilla option American/Option data and I found some European option which are more expensive than there American counterpart (all other factors are equal, except for the ...
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1answer
40 views

Domestic and foreign interest rate; dividends?

The spot price AUD/USD is 0.6868, strike price is 0.6915,the 6 month ATM implied volatility for AUD/USD is 7.7% p.a., for the 6 month USD deposit rate is 2.28% and the 6 month AUD deposit rate is 1.45%...
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1answer
53 views

Difference between modelValue from HestonModelHelper and NPV() from VanillaOption

I am trying to calibrate an Heston model and price vanilla option using Quantlib 1.15 and Python 2.7. I use the following code ...
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0answers
65 views

Valuation of Callable Bonds

Is there any way to price American Callable Bonds (those which can be called on any date before expiration) other than basic CRR interest rate trees, since they won't be accurate enough to give ...
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58 views

Deriving the black-scholes formula for the European asset-or-nothing call option

I would like to find out what boundary/final conditions i should be using to find the formula for a European asset-or-nothing call option, as i feel that is where I'm making my mistake. I've read ...
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62 views

Kirk Spread Approximation, Greeks by Finite Difference

I am using finite difference on Kirk's Approximation for Spread Options to estimate greeks of the Spread Option. Now this is creating an problem in the estimation of gamma. For at the money options (...
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0answers
47 views

Multiple layer Monte Carlo Option pricing

I have simulated 10000 price paths from the SVCJ model under $\mathbb{Q}$ from $S_{t0}$ until $S_{tm}$ and have computed one discounted option price $C_t$. I want to compute the numerical simulated ...
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41 views

Free Call Option [duplicate]

Suppose we follow the assumptions of the Black-Scholes Model, including unlimited borrowing, continuous prices, and frictionless markets. For simplicity assume the risk-free rate is 0. In this world, ...
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1answer
89 views

zero-shift SABR vega and re-calibration of SABR

I have a zero-shifted SABR model, where I need to confirm if the model is generating the calibration and vega's correctly. The underlying model is the standard SABR lognormal (there is normal as well)...
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2answers
52 views

Construct a portfolio of European call options with a certain payoff function

My question is similar to Replicate a Portfolio with Given Payoff but I am not quite sure how to apply this to my problem. A portfolio of European call options on an asset $S_T$ has a payoff ...
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2answers
180 views

How to calculate implied correlation via observed market price (Margrabe option)

I can't seem to figure out how to do the following: compute the implied correlation $ρ_{imp}$ by using the observed market price $M_{quote}$ of a Margrabe option, and solving the non-linear equation ...
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24 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 ...
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52 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, ...
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2answers
187 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
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2answers
108 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 ...
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1answer
121 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 ...
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2answers
156 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 ...
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1answer
53 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 ...
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1answer
188 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 ...
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47 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 ...
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1answer
63 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 ...
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1answer
157 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 ...
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1answer
90 views

European put options

Why is it that for European Puts on Non-Dividend-Paying Stocks, the lower-bound for price is $$p=Ke^{-rT}-S_0?$$
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2answers
242 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 $S$, $\sigma$ ...
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1answer
58 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 ...
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1answer
119 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. ...
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1answer
213 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)...
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1answer
112 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 ...
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2answers
242 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,...
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1answer
295 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 ...
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3answers
286 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 ...
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1answer
93 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(...
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144 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(\...
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0answers
73 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 ...
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1answer
165 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 ...
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0answers
27 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 ...
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1answer
672 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 ...
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2answers
110 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 ...
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91 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 ...
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1answer
131 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 ...
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83 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?...
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1answer
67 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 ...
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0answers
106 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
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1answer
293 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 ...
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1answer
420 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 ...
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1answer
383 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 ...
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1answer
68 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 ...
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0answers
100 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=...
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1answer
121 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 ...