Skip to main content

Questions tagged [black-scholes]

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

Filter by
Sorted by
Tagged with
0 votes
1 answer
32 views

time value of option proportional to sqrt(time)

I'm reading Natenberg's Options Pricing and Volatility, and in Chapter 18, he mentions this about an example: We can further refine our approximation if we note that an at-the-money option is made up ...
APerson's user avatar
0 votes
1 answer
43 views

Quantifying Costs/Benefits Of Partial Hedging

Say I sold a long-dated European put option and I want to analyze the costs and benefits of partial hedges in a world with stochastic price movements, rate movements, and volatility. For example, let'...
Mild_Thornberry's user avatar
-1 votes
2 answers
62 views

Proof of the value of an option using hedging and no-arbitrage [ Paul Wilmott Chapter 3.12.2]

I encounter a difficulty in understanding the proof of finding the value of an option. Before going into the proof, let's talk above the assumptions and parameters of the model. Assume that we know ...
Ricky Pang's user avatar
0 votes
1 answer
71 views

Expectation of average, conditional on terminal value

Silly question, but for some reason I'm a bit uncertain about this this trivial example perhaps: I have the following simple BS model $$ S_T = S_t \exp \left\{ -\frac12 \sigma^2 (T-t) + \sigma (W_T - ...
Frido's user avatar
  • 1,866
0 votes
1 answer
38 views

Negative Dupire Variance

I want to compute Dupire Local volatility using the identity that links Dupire local variance to BS implied total variance. I calibrated an SVI on options data to get the implied total variance ...
M2000's user avatar
  • 1
2 votes
1 answer
103 views

Preferred Option pricing model [closed]

I am at Uni studying mathematical finance and wanted to know which is most preferred /widely used model by Finance Industry Practitioners from the list below. Fourier Transform for option pricing ...
dijoney J's user avatar
0 votes
2 answers
62 views

stdev of delta hedged portfolio for call option !=0. Why?

I wrote a Monte-Carlo simulation of delta hedging for a european call. R and Sigma are fixed. I start simulation with zero money and short call option. At each step I borrow money to buy 'delta' of ...
lkjldfkjhljk's user avatar
0 votes
1 answer
91 views

Is the Black Scholes PDE actually immediate from Ito's lemma?

Ito's lemma replaces $dS^2$ by $vol^2*dt$, however it is repeatedly mentioned that the lemma manifests in the integral form and the differential form below is merely a short hand for the integral form:...
Arshdeep's user avatar
  • 2,212
0 votes
1 answer
100 views

Can a Call and a Put with same strike price and expiration date and underlying asset have different implied volatility?

Furthermore, assume that the current price of the underlying asset equals the strike price of the options. If volatility measures variance without a direction, it doesn't make sense to me that the ...
Lay González's user avatar
0 votes
0 answers
37 views

Barrier Puts Pricing (down-and-in put)

I am trying to price the down-and-in put option with European Style (when barrier level < strike price) by using Black Scholes Option Pricing model. but after checking the formula several times, I ...
Wannapat P.'s user avatar
0 votes
0 answers
78 views

How to access the Black Sholes Formula through the Distributive Law?

Recently I read a comment on how to interpret the Black Sholes Formula and more specifically how to wrap your head around the d1/d2. Although there were many good comments, this one stood out when one ...
Telefondemonen_se's user avatar
1 vote
1 answer
83 views

Martingale property of the CEV model

I am a bit confused about the martingale property of the CEV model. Given $dS(t)=σS(t)^βdW(t)$, is $S$ a martingale for values of $β<1$?
Atone202's user avatar
0 votes
2 answers
68 views

Obtain B-S-M from a binomial tree as n goes to infinty using Lebesgue integral

My question is simple, consider a European call with payoff max(S_T-K, 0), Let's suppose that the underlying stock follows a binomial tree with up and down factors I know as we take n goes to infinity ...
nic's user avatar
  • 1
3 votes
1 answer
176 views

How to estimate Dealers’ Gamma Positioning

I am new here so please forgive my basic question. There are many websites and experts out there that estimate dealer gamma positions, but I don't know what they are doing. I think I understand the ...
Suzume's user avatar
  • 31
1 vote
0 answers
94 views

Real options: discount rate for the value of the underlying security

This is an example inspired by Chapter 3, sub-chapter "Combining decision trees with real options(DTRO)", sub-sub-chapter "Case 4 Part Two", of Boer, F.P., 2004. Technology ...
robertspierre's user avatar
0 votes
0 answers
27 views

Black scholes, issues inferring T(time to expiry) andS (underlying price)) from wrds SPX dataset

I'm working on a project with the SPX option data from wrds. This data doesn't provide the underlying price at the time of the observation, or the time to expiry at the time of the observation. ...
steve_nash's user avatar
0 votes
0 answers
99 views

How do I calculate the implied dividend yield and/or the forward rate for an equity ETF?

I am interested in building an implied volatility surface for a given ETF given a set of option prices for several combinations of (call/put,strike,expiry). I am interested in different ways to arrive ...
quantypythonshow's user avatar
1 vote
1 answer
101 views

How should I go about computing the 30-day model free implied volatility (MFIV) daily?

As the title suggests, how can I calculate the MFIV daily (for a market index)? My MFIV follows the procedure described in DeMiguel et al. (2013) Improving Portfolio Selection Using Option-Implied ...
KaiSqDist's user avatar
  • 1,312
1 vote
0 answers
75 views

Does it make sense to use Black Scholes greeks to attribute P/L given the Black Scholes assumptions don't hold?

I've seen some takes from experts in the industry (Benn Eifert for example) who say that we should treat Black Scholes as a translation mechanism for putting price into a more workable form (IV). They ...
mrdrralph's user avatar
  • 121
1 vote
1 answer
135 views

Prove from Black-Scholes that value of a European call option on an asset that pays continuous dividends less than a call without dividends

Black-Scholes gives us the following formulae for the prices of European calls on an underlying that does or doesn't pay continuous constant dividends (of proportion $D$): $$C^E_D(S_t,t,K,T)=e^{-D(T-t)...
hegash's user avatar
  • 111
0 votes
0 answers
31 views

Tradeability of Option (not underlying) necessary assumption in BSM?

Working with the Black Scholes Model to value european Call and Put Options I encountered a question that came up during the valuation of a (european Call) Option, which itself cannot be traded (e.g. ...
Frank's user avatar
  • 1
1 vote
1 answer
170 views

The partial derivative of a call option with respect to $t$ [closed]

In Black-Scholes related computations, why do we not treat the stock price $S$ as a function of $t$ when taking partial derivatives with respect to $t$? For example, if $$c(t,T)=SN(d_1)-Ke^{-r(T-t)}N(...
user81883's user avatar
  • 111
0 votes
1 answer
106 views

Can someone please help me answer this question about Black-Scholes model? (risk-neutral & true probability of the call option) [closed]

I don't even know where to get started with this question...can someone please help me? How do I answer it?
Jolie's user avatar
  • 1
0 votes
0 answers
97 views

Positive Theta for an At The Money option (with real data)

Ive been doing some work on looking at historical options prices on a stock index using real data, and I came across an odd example that I cant really get my head around. I am aware that for extreme ...
Arron's user avatar
  • 1
0 votes
1 answer
51 views

Black-Scholes model portfolio position

Question: I am a physicist currently learning about the Black-Scholes model in a statistical mechanics course. I have been teaching myself financial terminology and was reading the "Derivation of ...
Patrick's user avatar
  • 11
0 votes
0 answers
71 views

About Hedging of One-touch Options

The pricing of American Digital Call (one-touch Calls) has the following formulas, taken from P13, the textbook \begin{aligned} C_{\mathrm{d}}^{\mathrm{Am}}(S, t ; E) & =\left(\frac{S}{E}\right)^{\...
newbiesolidty's user avatar
1 vote
1 answer
89 views

Seeking Advice on Normalizing Implied Volatility Change for Options Modeling

I'm working with a substantial dataset spanning five years of weekly options data, with records down to the second. My goal is to develop a model that can accurately predict the probability mass ...
Manish Arora's user avatar
0 votes
1 answer
57 views

In Black-1976, why is the differential equation missing a term relative to B-S?

In the notation of the original Black-Scholes paper, let $w(x, t)$ be the price of an option with underlying priced at $x$, and let $w_1$ denote the derivative of $w$ w.r.t. to $x$ and $w_2$ denote ...
jds's user avatar
  • 138
2 votes
1 answer
212 views

Hedging gamma, theta or other risks

Speaking on a high level, in the Black-Scholes model the $f\left(T,S_{T}\right)$ payoff's value dynamic is given by $$df\left(t,S_{t}\right)=\left(\frac{\partial f}{\partial t}\left(t,S_{t}\right)+\...
Kapes Mate's user avatar
0 votes
0 answers
50 views

Real Options for investment valuation (Basics)

Thank you for checking out this post. I already asked a question once on this forum, and you did a great job helping me out with that topic, as I couldn’t have come across a solution myself. This time,...
Bourrinou3's user avatar
2 votes
1 answer
99 views

Why A Derivative With Intrinsic Arbitrage Cannot Be Valued & Hedged With Assets In Risk Neutral?

I'm attempting to concisely show why a derivative that, by nature, introduces arbitrage cannot be valued using risk neutral pricing tools. Derivative: Buyer is sold a 'call option', with time 0 value ...
TheOneTwoThreeForPumpkin's user avatar
0 votes
2 answers
127 views

Trying to follow course notes deriving Black-scholes PDE, but I can't fill in the gaps

I'm a math master student. I'm trying to follow a course-note that unfortunately has chasms to fill for this specific derivation. Rigour unfortunately has been thrown to the gutter. Let $G$ denote a ...
AyamGorengPedes's user avatar
0 votes
0 answers
33 views

Model for markets with friction

Is there a stochastic model for describing how equities behave in markets with trading fees, and if so what model is most commonly used? I'm envisioning something similar to the Black Scholes model, ...
djr's user avatar
  • 1
0 votes
1 answer
118 views

Geometric Brownian motion with volatility as function of time

With the following process: $$dS_t = r S_t dt + σ(t) St dW_t \tag1$$ and $$ \sigma (t) = 0.1 \ \ \ if \ \ t < 0.5 \\ \sigma (t) = 0.21 \ \ \ otherwise$$ I know the general solution should be : $$...
TJT's user avatar
  • 103
2 votes
1 answer
208 views

Black Scholes derivation and Ito's Product

In this derivation of the Black Scholes equation can someone please explain the last step where the author uses Ito's product rule? I do not understand where the "rC" term comes from.
Ria's user avatar
  • 23
0 votes
1 answer
320 views

Risk free rate for Black and Scholes model: Incorporating inflation?

I am new to quantitative finance and I am trying to create a model for option pricing. Naturally the Black and Scholes equation is front and center for this sort of thing, but that raises the question ...
SSC Fan's user avatar
  • 53
1 vote
1 answer
151 views

Connection between the $\sigma$ parameters of the spot price and the forward price

It is well known, that under the Black-Scholes framework: $$F\left(t,T\right)=\exp\left(r\left(T-t\right)\right)S\left(t\right),$$ where $S\left(t\right)$ is the spot price of an asset at time $t$, $F\...
Kapes Mate's user avatar
-2 votes
1 answer
195 views

perpetual American-style call option

Greek “phi” for a derivative f is defined as its sensitivity to the changes in dividend yield q : $$\phi = \frac{\partial f}{\partial q}$$ HOW CAN I FIND PHI WITHOUT THE CORRELATION?
user avatar
0 votes
1 answer
128 views

The metric to evaluate the efficiency of ANN based option pricing over mathematical option pricing models

The stock exchanges provide the data of option prices using theoretical formulations such as Black-Scholes formula. The dataset necessary for training an artificial neural network (ANN) to address ...
Messi Lio's user avatar
  • 113
0 votes
0 answers
77 views

Cash Dividend implies skewed (negative) vol smile?

Say we have a stock $S_t$ which pays a cash dividend at $T_D$ of amount $div$. Let us assume rates $r=0$, for simplicity. Then the forward is $F_{T_D} = S_0 - div$, and we can compute the continuous ...
Phil-ZXX's user avatar
  • 1,042
2 votes
2 answers
153 views

Price Option B Knowing The Price of a Similar Option A

How do we find the implied volatility from the price in a call option and apply it to another option without a calculator? Or is there actually a better way? For example, given a 25-strike 1.0-expiry ...
Kai's user avatar
  • 123
0 votes
0 answers
61 views

Risk-Neutral Non-Linear Option Pricing Black Scholes Model

Looking for some help on this question. Suppose the Black-Scholes framework holds. The payoff function of a T-year European option written on the stock is $(\ln(S^3) - K)^+$ where $K > 0$ is a ...
Kai's user avatar
  • 123
0 votes
1 answer
158 views

Why do the Greeks not converge to the strike as the volatility tends to zero? [closed]

So, I was playing around with the Greeks in Python with some made up data for a European call option assuming the Black-Scholes model. I plotted the graphs to see what happens to the Greeks when ...
Mr. Ivan's user avatar
0 votes
3 answers
142 views

Closed form / analytical solution for bespoke (but vanilla) Option

Question: I want to derive closed form expression (similar to the Black Scholes formula for a call price) for the payoff below. I would like to do it from first principles starting with Expectations ...
gmarais's user avatar
  • 121
0 votes
1 answer
149 views

How can I price this option? [closed]

In the Black-Scholes model, I want to price the so called Butterfly option, where the payoff $P(x)$ is the following function: $P(x)=0$ if $0\leq x\leq 40$, $P(x)=x-40$ for $40\leq x\leq 60$, $P(x)=-x+...
Summerday's user avatar
  • 105
1 vote
2 answers
509 views

0DTE volatility and greeks

When european stock options have very little time until expiration (less than 2-3 hours), they can exhibit extreme sensitivity to changes in the underlying asset's price. This behavior leads to ...
shoonya's user avatar
  • 141
0 votes
0 answers
167 views

Straddle Approximation - Directly from Integral

The ATMF straddle approximation formula, given by $V_\text{Str}(S, T) \approx \sqrt{\frac{2}{\pi}} S_0 \sigma \sqrt{T}$ where $S_0$ is the current underlying spot price, $T$ is the time remaining ...
aarongroff's user avatar
0 votes
1 answer
114 views

Black Scholes/American Put/Martingale Condition

Consider a Black Scholes model with $r \geq 0$. Show that the price of an American Put Option with maturity $T > 0$ is bounded by $\frac{K}{1 + \alpha} {(\frac{\alpha K}{1 + \alpha})}^{\alpha}{S_{0}...
Parinn's user avatar
  • 105
0 votes
0 answers
74 views

Analyzing the Impact of S&P Volatility Shift on ATM Straddle Sale: Calculating Loss/Gain[black scholes]

Black scholes:The 1-month implied volatility of S& ;P is 16. The slope of the skewness curve is -1 point per 1%; For example, the 99% exercise trades at a premium of 1 vol point. regarding the ...
Alexander's user avatar
0 votes
1 answer
73 views

When to use total derivative and when not to?

as I was trying to teach myself financial mathematics, I came across this topic on transforming black scholes pde to a heat equation. I had the exat same question as this post Black Scholes to Heat ...
David's user avatar
  • 1

1
2 3 4 5
24