Questions tagged [bachelier]

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2 votes
0 answers
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How did Bachelier characterize the Brownian motion?

The model for a stock price $$ dS_t=\mu dt + \sigma dB_t $$ where $B_t$ is a Brownian motion on $(\Omega, \mathcal{F},P)$, is commonly attributed to the work that Bachelier has carried out in his PhD ...
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2 votes
1 answer
307 views

Does it matter that Bachelier IV differs from BS IV for a given option price?

In one sense, it’s just an accounting convention, so it doesn't matter. In another sense, the implied volatility can be interpreted as the minimum realised volatility which implies that your option ...
0 votes
0 answers
44 views

Is there a modified Bachelier's futures spread option model with adjustments for skew and kurtosis?

I'm looking at pricing a very large deal and while the distribution is kind of "normal," there's quiet a bit of skew and kurtosis that isn't being considered when I use the normal Bachelier'...
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0 answers
68 views

Trades, quotes, and Prices: is high frequency noise scalable by price?

In Section 2.1.3 (page 27) of Trades, Quotes, and Prices by J-P Bouchaud et al., the authors introduce $\eta_t$, an uncorrelated noise term to Bachelier's First Law. In equation (2.13), the authors ...
0 votes
0 answers
276 views

Gamma, Theta, Vega, Vanna and Volga PnL under Bachelier

Is there a PDE that decomposes the daily PnL as delta, gamma, vega vanna and volga but under Bachelier model (assuming normal vol) ?
1 vote
0 answers
58 views

Which Model Should I Use for Pricing USD Interest Rate Caps (7, 10, 30 year maturities) on 1Month Rates?

I am trying to price USD interest rate caps on 1M rates (e.g., LIBOR, SOFR, etc.). The caps are designed to limit the exposure on non-callable USD Pay Float / Receive fixed positions in interest rate ...
3 votes
0 answers
394 views

Deriving Bachelier Greeks

I am working on the Bachelier Model with r not equal to 0 as described in the first and most upvoted answer in following link: Bachelier model call option pricing formula This is fairly easy to code ...
3 votes
1 answer
136 views

EMM for Bachelier model

The stock price is assumed to evolve as $S_{t}=S_{0}+\mu t+\sigma B_{t}$, where $S_{0}>0, \mu>0$ and the process $B_{t}$ is Brownian motion. The saving account is assumed to be $\beta_{t}=e^{r t}...
1 vote
0 answers
66 views

Sensitivities under Bachelier process

The sensitivity profile like (delta, vega, gamma etc.) of an option contract is quite established if the valuation model follow ...
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1 vote
2 answers
187 views

Method of comparing two option pricing models?

I am currently writing a small paper comparing the Black-Scholes formula to the Bachelier model. However I am wondering how exactly I should compare the two models? Obviously I am comparing the prices ...
0 votes
1 answer
217 views

Bachelier model call option pricing formula with leverage and spread

the call option pricing formula for the plain/vanilla payoff ($S_T-K)^+$) has been resolved, under the Bachelier model here: Bachelier model call option pricing formula But can anyone help me with ...
1 vote
1 answer
257 views

Bachelier model in terms of normal distribution to simulate price

Bachelier Model is $dS_t = rdt + 𝜎dW_t$ and can also write to $S_t = S_0 + 𝜎W_t$ How can write $W_t$ in terms of normal distribution? Basically I want to simulated the underlying asset in the ...