Questions tagged [black-scholes]

Black-Scholes is a mathematical model used for pricing options.

Filter by
Sorted by
Tagged with
2
votes
0answers
31 views

Determination of critical stock price in compound option pricing

Under the Black-Scholes framework, there is a closed form formula for the price of a compound options, as first derived by Geske (1979). However, the analytical formula refers to a critical stock ...
0
votes
1answer
78 views

How to understand broken wing butterfly option strategies?

I feel very confused about the greeks analysis for the broken wing butterfly strategy. Let's say for the stock ABC, we enter into a such strategy: we long a put option with strike $k_1$ and another ...
2
votes
1answer
316 views

Exercise Probabilities Vanilla Cap/Floor

When looking at the discounted pay-off formulas of a vanilla caplet and a vanilla floorlet $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_k-r_{cap},0)$ $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_{floor}-...
-3
votes
0answers
49 views

Worst-off Options [closed]

I´m working with worst-off options. I´d like to know if I should expect a difference in valuation between WO(call1(S0=100,K=100,vol=20%,rf=0,T=1),call2(S0=100,K=100,vol=20%,rf=0,T=1)) and WO(put1(S0=...
2
votes
1answer
93 views

Calibrate Stochastic Volatility Model

For stochastic volatility models, and any vol model I know, it seems the standard approach is to calibrate the model from option prices. As other user said, this seems a chicken egg problem - how do I ...
0
votes
1answer
44 views

Finding option price using intraday data [closed]

I have the option price at a rate which is much smaller than the rate at which I have tick data for the underlying. If I have option price at times $t_1, t_3, t_5$ and I have tickdata at $t_1, t_2, ...
1
vote
0answers
45 views

Black Scholes implied volatility [closed]

I am reading up on implied volatility and I encountered the term Black-Scholes implied volatility which I haven't heard before. What is the meaning of this term? Say I am looking at the Heston model ...
1
vote
0answers
71 views

Pricing of an option

I've priced a European option with payoff $\max\{S_T(S_T - K), 0\}$ and found $S_0(S_0 \exp((r + \sigma^2)T) \mathcal{N}(d_3) - K\mathcal{N}(d_1))$ where $d_i = \frac{\ln(\frac{S_0}{K} + (r + \frac{i\...
1
vote
0answers
28 views

Expected life (Fugit) of American Option

How can I use the binomial tree pricing method for American options to determine the expected time of exercise for the option (or "Fugit")? In particular, how would I modify the algirithm ...
0
votes
0answers
33 views

variance of asset returns linear for time

I am reading Wilmott's book, "Quantitative Finance" and try to understand the derivation that the variance of asset-returns, $V[\Delta S/S]$, is a linear function of the time step $\delta t$....
0
votes
0answers
52 views

Quantity of risk-free asset in Black Scholes model

When the seller of a Call option hedges themselves, we know that they should buy $\Delta(t) = \mathcal{N}(d_1(t))$ amounts of the risky asset at time $t$. But what about the riskless asset? My ...
1
vote
1answer
76 views

Why does black scholes model give lower prices for puts with further time to expiry?

Consider BS-model with parameters: Stock = 100, Strike = 100, Texp = 1 year, Vol = 13%, Rf Rate = 3%. For these parameters the BS put price is 3.76. Then consider the same parameters but with Texp = ...
0
votes
1answer
59 views

Computing the Probability Density Function (PDF) for the Heston model

I am trying to compute the PDF for the Heston model using the Breeden Litzenberger formula. I have calculated the the Heston implied volatilities for a strike range (which i have interpolated using ...
0
votes
0answers
40 views

Error in Call Option Valuation using Implicit Finite Difference implemented in Python

I am trying to valuate call option using implicit Finite difference method (Forward Marching) implemented in Python. However I am getting the error in the code. Following is the code I have developed: ...
0
votes
0answers
30 views

How do I hedge two/three zero coupon bonds with different maturity under Vasicek short rate model?

I am working on the case that I need to hedge two bonds with different maturites under Vasicek model, which is \begin{equation} dr_t=a(b-r_t)dt+\sigma dW^Q_t \end{equation} and I know how to price the ...
0
votes
1answer
58 views

How to extrapolate shorter tenor from volatility surface?

Overnight(ON) volatility is the first input of a volatility surface, 1 weeks, 2 weeks and so on... Say I have a volatility surface with ON expiry of 1 day, is there anyway to extrapolate volatility ...
3
votes
1answer
84 views

Asian option sensitivity

I am looking for some materials for profiling all options sensitivities for Asian options with both geometric averaging and arithmetic averaging . The underlying price $S_t$ follows a standard GBM. Is ...
0
votes
1answer
106 views

Estimation of volatility into Black-76 formula

I am trying to estimate the (annualized) volatility that should go into an European Swaption (such as 2y5y). Given we take the black76-formula, where the discounting is the term outside the ...
0
votes
1answer
95 views

Black-Scholes and solving for both $r$ and $\sigma$ ; Do I have a unique solution?

Below is a problem that I am working on. I believe that my incomplete solution is correct as far as it goes. I would like to know if my solution is incorrect. I plan to solve the system of two ...
0
votes
1answer
98 views

Black-Scholes formula given arbitrary value of $S_{T}$

Is there a formula for Black and Scholes when we have expected payoff $\mathbb{E}[\max(se^{X}-K,0)]$ for $X$ having any normal distribution?
0
votes
0answers
33 views

Hedging costs and BS-price

I'm looking at the chapter, "The Greek Letters" in Hull's book (Options and derivatives...) and in particular the paragraph "Dynamic Aspects of Delta Hedging". He demonstrates two ...
1
vote
1answer
131 views

Black Scholes to Heat Equation

Equation (2) was derived by setting r=0 in the Black-Scholes equation for the Bachelier model (1). Can someone please help me understand all the steps for how we get from the heat equation under time ...
0
votes
0answers
29 views

Breakdown of Wilmott's Binomial Tree derivation of Black-Scholes equation

Hi guys, I tried to follow the chapter of PWIQF on binomial model and got stuck when it derived the Black-Scholes (please see image). I tried to backtrack the said equations but couldn't trace back ...
0
votes
0answers
21 views

Value in time of the bond in delta-hedging

I am trying to implement a simple delta-hedging strategy. The idea is that I want to verify that the covered position "1 option long + delta stocks short" is actually evolving as $e^{rt}$, ...
0
votes
0answers
33 views

Estimating dividend yield & risk-free rate from Futures prices

I would like to work with the dividend-adjusted Black Scholes formula and need to estimate the dividend yield and risk-free rate. I know that I could compute both rates exogenously. But I am working ...
1
vote
1answer
718 views

Probability of exercise in the Black-Scholes Model

What's the intuition behind the fact that the limit of $\mathcal{N}(d_2)$, i.e. the (risk-neutral) probability of exercise, in the Black-Scholes Model tends to $0$ when the volatility tends to ...
0
votes
0answers
35 views

Using EOINA, €STR for option valuation

for an assignment I have to value options using an OIS rate using the Black-Scholes model. Since my options are traded in Germany I was looking at the EONIA or newly €STR. (Since Hull 2012 recommends ...
1
vote
2answers
304 views

What is the price of the European option with the payoff of $\max(S^a-K,0)$?

I interpret such an option as a power option but I do not find any literatures or existing methods to price it. Can it be priced with Black-Scholes with simple changes?
1
vote
1answer
130 views

Arithmetic Asian Option

Assume the risk-free bond Bt and the stock St follow the dynamics of the Black & Scholes model without dividends (with interest rate r, stock drift $μ$ and volatility $σ$). Let $A_T:=\frac{1}{T}...
1
vote
0answers
71 views

Option that never expires

I have been struggling with the problem below for quite some time now. I really don't know how to approach it. All I could think of is to use the Black-Scholes formula with $T \rightarrow \infty$, ...
1
vote
2answers
66 views

Volatility estimation based on a 60 days range

In Hutchinson et al: A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Network (1994) paper (link), to estimate $\sigma$ for the Black-Scholes formula, it says (p. 881)...
4
votes
2answers
3k views

Why gamma and theta have opposite signs?

I saw some textbooks use B-S equation to explain why gamma and theta have opposite signs in most of the cases. For example, John Hull's classic book. The explanation is, first write B-S equation in ...
2
votes
0answers
55 views

Stocks with same volatility but different drifts

In the book Quant Job Interview Questions & Answers, in section 2, question 2.4 says suppose two assets in a Black-Scholes world have the same volatility but different drifts. How will the price ...
2
votes
1answer
304 views

Relationship between asset volatility and debt and equity value

So how I understand it, higher asset volatility implies a higher call option price. The Merton Model holds that the value of equity is a call option. This therefore implies that the equity value must ...
1
vote
4answers
446 views

Delta hedging pnl to recover option price

In Black Scholes framework, assuming zero interest rates and realized volatility to be same as implied volatility, gamma pnl is exactly same and opposite of theta pnl. So if I buy an option and delta ...
2
votes
1answer
91 views

How to calculate dividend yield - option pricing

Hey how do you calculate the dividend rate if you want to price your stock options eg apple? Just take the dividends paid last year and divide by today's share price? This page reports 0.85% (https://...
0
votes
1answer
45 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 ...
1
vote
1answer
67 views

Over-night Black-Scholes

I have a question for Black-Scholes. It is a continuous approach, but the real market closes every day. So for the Black-Scholes, how do we count the time effect of during the time when the market is ...
2
votes
2answers
274 views

Market price of risk on two assets

Under the assumptions of the Black--Scholes model, I read that the market price of risk of two assets $S_1$ and $S_2$ are the same, if they both follow Geometric Brownian motion driven by the same ...
0
votes
0answers
41 views

Black Scholes model calibration

the only parameter in the Black Scholes model that needs to be estimated is the volatility. Which approach is correct: Estimation of volatility from daily log returns Estimating volatility by ...
2
votes
3answers
187 views

Arbitrage Condition and Identity in Black-Scholes

After I went through the derivation to get the skew in Backus et al., I had two questions: In the proof, it mentioned the application of the arbitrage condition and then obtained equation (31): $$\...
2
votes
1answer
91 views

Black-Scholes Formula under $T$-forward measure

The Black-Scholes price of a European call option is given by $$ C_0^{BS}(T, K) = \mathbb{E}_Q[e^{-rT}(S_T - K)_+] = S_0 \Phi(d_1) - Ke^{-rT}\Phi(d_2) ,$$ where $$ d_{1,2} = \frac{\log\big(\frac{S_0}{...
4
votes
1answer
123 views

Can “Turbo warrants” be priced using the Black & Scholes model?

I am trying to model the pricing of an asset called a "Turbo warrant", which to me looks a lot like a Down-and-Out Barrier option with leverage. When the price of the underlying asset hits a ...
0
votes
2answers
62 views

I just got Matlab, what are some options that I should model in a jump diffusion

Don't worry I understand mathematics: ito's calc, martingales, etc. I am just curious what options I should test, and from what indices. Is there stuff I can test from the 2008 crash to measure their ...
0
votes
1answer
99 views

VBA Black Scholes Implied Volatility

I keep getting a Implied Vol. = to my initial guess, My code is as bellow ...
1
vote
1answer
99 views

Are there stocks dynamic that cannot be represented by Generalized Black Scholes model?

The generalized Black Scholes Model refers to a stock dynamic that satisfy $$ dS(t)=S(t)(\mu_t dt+ \sigma_t dW(t)) $$ By martingale representation theorem, it seems that if there is a risk neutral ...
3
votes
0answers
2k views

Black-76 Model for Swaption Price and Greeks

I'm in the early stages of developing a swaption pricing model. Suppose $t_1$ is the tenor of the swap rate in years, $F$ is the forward rate of the underlying swap, $X$ is the strke rate of the ...
3
votes
0answers
72 views

Operator splitting method on three assets black scholes equation

Currently I am studying finite difference method on derivatives with three (or more) underlyings and little bit confused on operator splitting method because two papers have different result. For the ...
0
votes
2answers
78 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 ...
4
votes
2answers
201 views

Hedging with different volatility (Ahmad and Wilmott paper)

In their paper they show that: - if you hedge with the realised volatility, the present value of the total p&l is the difference between the option value based on the realised volatility and the ...

1
2 3 4 5
18