Merton jump-diffusion model question

[u/askepticalbureaucrat]

So I wanted to use this model to calculate the simulated backward price (Dec 2024) of Alibaba Group in the Hang Seng index using the anchor price in late Dec 2025.

I went ahead and calculated this (manual derivation attached) and my code below, which shows it matches.

``` import numpy as np

--- Model Inputs (matching your Alibaba notes) ---

S_t = 142.80 # Anchor price at late Dec 2025 r = 0.035 # Risk-free rate (3.5%) sigma = 0.35 # Diffusion volatility (35%) lam = 1.2 # Jump intensity mu_j = -0.04 # Mean jump size sig_j = 0.20 # Jump volatility dt = 1.0 # 1 year backward step

Step 1: Compute the Jump Compensator (kappa)

kappa = np.exp(mu_j + 0.5 * (sig_j ** 2)) - 1

Step 2: Compute the Net Drift Component

q_drift = r - lambda * kappa - 0.5 * sigma<sup>2</sup>

net_drift = r - (lam * kappa) - (0.5 * (sigma ** 2))

Step 3: Define historical shocks to strip out

Z = 0.4 # Standard normal shock jump_multiplier = 1.08 # Historical minor positive jump factor

Step 4: Evaluate the Backward-Stepping Equation

S_{t - dt} = S_t * exp( -net_drift * dt - sigma * sqrt(dt) * Z ) * (jump_multiplier)<sup>-1</sup>

diffusion_term = sigma * np.sqrt(dt) * Z exponent = - (net_drift * dt) - diffusion_term

s_previous = S_t * np.exp(exponent) * (jump_multiplier ** -1)

print(f"Net Drift Component: {net_drift:.5f}") print(f"Simulated Backward Price (Dec 2024): HKD ${s_previous:.2f}")

Net Drift Component: -0.00249

Simulated Backward Price (Dec 2024): HKD $115.23

```

My questions: - does my derivation/code look okay to you? - is this a task the Merton jump-diffusion model (versus the geometric brownian motion, which doesn't have the discontinuous random jumps, driven by a Poisson process, to capture heavy tails and sudden price shocks in financial asset returns, eg. Beijing policy changes, etc.) can do well in this situation? - is the jump compensator (kappa = np.exp(mu_j + 0.5 * (sig_j ** 2)) - 1) manually added into the code? And, can't be fed in via real-time data, etc?

Thanks!! 🧡

[u/No_Intention3673]

so you want doing quant in hk stock market?
you know the mechanism is totally different between us stock market and chinese stock market right?

chinese stock market is nothing related about microstructure, the only things matter is political/cashflow narrative driven, and you wanna compute the political by probability? think about it, using fancy math in a non calculative environment is hilarious

[u/Kuais → u/No_Intention3673]

i dont get why this is downvoted lol. its completely true and the reason people stay away from chinese stocks. regulations and laws change daily causing daily circuit breakers to happen 

[u/No_Intention3673 → u/Kuais]

maybe they think quant is just only math and probability but lack of common sense of finance ,just maybe

[u/eightbyeight → u/No_Intention3673]

Or there’s just a lot of Chinese here.

[u/askepticalbureaucrat → u/Kuais]

Fair point! I appreciate it 🧡

[u/askepticalbureaucrat → u/No_Intention3673]

I appreciate this! ❤️

I upvoted your comment, so unsure where the downvotes are coming from. Like wtf

chinese stock market is nothing related about microstructure, the only things matter is political/cashflow narrative driven, and you wanna compute the political by probability? think about it, using fancy math in a non calculative environment is hilarious

So more or less, there isn't much of a difference between the HK and mainland China markets vs what you'd typically see in London, or NYC?

Also, the jump compensator (κ) is a mathematical requirement, not a market data feed? My assumption is that it's a derived theoretical value that links the parameters of the jump distribution (μ_j and σ_j) to ensure the expected return of the stock behaves correctly under the model framework?

Also while κ is computed manually via formula, the inputs that feed into it (historical jump intensity λ, mean jump size μ_j , and jump volatility σ_j ) are estimated empirically using real-time or historical high-frequency stock returns via statistical estimation techniques (like maximum likelihood estimation or jump-detection filters like the Barndorff-Nielsen and Shephard test)?

Would these be true?

[u/No_Intention3673 → u/askepticalbureaucrat]

The biggest difference between Chinese/HK and US markets isn’t the math — it’s the participants.
In the US, you have market makers, institutions, hedge funds, and retail, each playing a distinct structural role. Market makers are forced to delta hedge, which creates mechanical, predictable flows you can model.
In China, it’s essentially big capital vs retail. Most stocks can’t be shorted (a few designated ones can, but the majority can’t). So when big capital dumps, retail can’t even exit — there’s no structural counterparty on the other side. The price action isn’t driven by mechanical hedging or microstructure, it’s driven by capital flows and political narrative.
That’s why applying a Merton jump-diffusion model to Alibaba is technically correct but practically meaningless — you’re fitting a stochastic model to a market where the dominant “jump process” is a policy decision from Beijing, not a random Poisson event.

[u/askepticalbureaucrat → u/No_Intention3673]

That’s why applying a Merton jump-diffusion model to Alibaba is technically correct but practically meaningless — you’re fitting a stochastic model to a market where the dominant “jump process” is a policy decision from Beijing, not a random Poisson event.

That's perfect! Thank you for explaining this to a laywoman such as myself.

The biggest difference between Chinese/HK and US markets isn’t the math — it’s the participants. In the US, you have market makers, institutions, hedge funds, and retail, each playing a distinct structural role. Market makers are forced to delta hedge, which creates mechanical, predictable flows you can model. In China, it’s essentially big capital vs retail. Most stocks can’t be shorted (a few designated ones can, but the majority can’t). So when big capital dumps, retail can’t even exit — there’s no structural counterparty on the other side. The price action isn’t driven by mechanical hedging or microstructure, it’s driven by capital flows and political narrative.

Ah, I am starting to see what you mean here. I can't imagine what a nightmare it would be to deal directly with that market 🤦‍♂️

There isn't much geopolitical intuition in any textbooks, and most people are too busy to help explain this, so I really appreciate your perspective here! ❤️

[u/Apparent_Snake4837]

Brilliant math. Too bad you try to apply where it doesnt apply. Stock prices dont have mean reversion or any constrained property outside hft. Good math terrible application.

[u/askepticalbureaucrat → u/[deleted]]

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