Chapter 434: The Model

April 9th, the weather was as good as ever. The branches on both sides of the Charles River sprouted new buds, and dots of green dotted the branches.

Inside the house, Er Miao was attracted by the bird chirping outside the window, pricked up its ears to listen a few times, then turned to look at the two-legged beast with a calm expression, dismissed the idea of asking for a hug, and drooped its head to continue napping.

Xu Qingzhou carefully read the materials and papers Song Yao gave him.

He had a general idea of his work.

Composite options involve multiple decision points, and each stage's decision affects subsequent paths, so path dependency is very strong.

Multi-stage means there may be multiple option execution points, such as different stages of R&D projects, namely clinical trials phase I, II, and III. Each stage has the choice of continuing, abandoning, or expanding.

The difficulty lies in high-dimensional state space, path dependency, computational efficiency, numerical stability, etc., especially how to model reality's uncertainty as a stochastic process.

At noon, after simply stir-frying two dishes and finishing them, he had already helped the school beauty check the Bayesian hierarchical model that had been done, and looked at the code again.

【#Parameter setting

(42)

t=3#Number of R&D stages

mu_d=0.1#Market demand growth rate

sigma_d=0.3#Volatility

p=100#Vaccine unit price (USD/dose)】

【#Generate market demand paths (Geometric Brownian Motion)

defgenerate_demand_paths(d0=1e6, t=10, dt=0.1, n_paths=n_sim):

steps=int(t/dt)】

"Using PyMC3, Bayesian stage success rate update..." Xu Qingzhou stared at the jumping code on the computer screen and gasped, "It's done perfectly."

It had to be said that Song Yao's mathematics was quite amazing.

The model was concise, without redundant descriptions... This might be the talent-type player.

He shook his head, picked up a pen, and wrote down the representation formula for project value (v) in the Monte Carlo simulation mathematical model.

【v=\max_{au}\math+e^{-rau}\phi(s_au)\right】】

Two days passed quietly. Xu Qingzhou spent most of his time doing Song Yao's mathematical model, or acting as a nanny for the school beauty, doing some cooking.

Song Yao's period was generally around the 2nd.

But in order to be lazy and order her boyfriend around, she could drag her period until the teens.

It was simply openly pretending to be weak.

At 6:00 PM, Song Yao sent a message asking: "I'm back, is there anything you want me to bring?"

"Cola and fried chicken." Xu Qingzhou struggled for a while, really couldn't think of anything to eat, so he just chose the old set meal.

Song Yao rejected: "No, change one."

It was indeed eaten just yesterday evening.

Xu Qingzhou typed: "You buy whatever; I'm easy to raise."

Song Yao replied with a cold "Good."

Xu Qingzhou just waited to be fed, his gaze on the manuscript on the side. The mathematical model needed for the school beauty's paper was quite tedious, estimated to take about a week to finish.

Forty minutes passed.

Song Yao returned carrying a plastic bag. Xu Qingzhou glanced at it; inside were noodles and green vegetables. He said: "I thought about it, it's better to cook it myself..."

"Want to cook? Has your body recovered?" Xu Qingzhou asked lazily.

Song Yao curled her lips: "Do you want to eat or not?"

"Eat. If you drag it on for a few more days, I'll be worried about you being anemic."

"Shut up."

"Okay."

Song Yao cooked two bowls of tomato and egg noodles.

Because of weight loss, Song Yao only ate half a bowl and rested her chin on her hand to watch her boyfriend.

This guy finally recovered some energy, not in the decadent state he was in a few days ago.

She asked: "Any problems in the calculation?"

"Already finished a part, let's look at it together in a while. Just right, I really encountered two places I didn't understand; you explain them to me."

Xu Qingzhou slurped the noodles, originally wanting to chew a clove of garlic, but held back.

"You have things you don't understand?" Song Yao's eyes revealed surprise. Having been together for so long, there was always a feeling that this guy knew everything.

"I'm not an economics major; isn't it normal not to understand?"

Xu Qingzhou cleaned up the bowls and chopsticks, while Song Yao sat at the computer to look at Xu Qingzhou's results from these few days.

"Seems... all quite good."

Song Yao finished looking at the model and looked back at her boyfriend in the kitchen hesitantly.

Soon, Xu Qingzhou came out wiping his hands. She stood up and gave the seat to Xu Qingzhou. "Tell me, where don't you understand?"

Xu Qingzhou pulled Song Yao to sit on his lap. "You check this part of the content first."

"Finished looking." Song Yao felt more and more that this guy had no good intentions.

"The paper must be rigorous; I'll explain it to you carefully."

Xu Qingzhou wrapped his arms around her slender waist. "Through sparse prior distribution, using Laplace prior, reducing parameter dimensions... However, here, here, and here, I don't quite understand."

Song Yao's eyes drooped, sweeping over the claws that had burrowed into her clothes, trying hard to keep her breathing steady, and explained with concentration: "At different stages of R&D, when to continue investing or abandon the project requires solving the Bellman equation..."

"With real option pricing as the core, it integrates multi-dimensional theories such as risk-neutral pricing, Bayesian learning, capital budget optimization, and market failure correction."

"Because biomedical projects lack liquidity, I want to reverse-calibrate the risk price through the volatility of the biotech ETF."

"Xu Qingzhou~"

Song Yao's voice suddenly trembled a bit.

"Mm, Song Laoshi, continue, I'm listening carefully."

Xu Qingzhou nodded as if nothing happened, the faint scent of fragrance attacking him. He glanced sideways at the school beauty. Song Yao's facial lines didn't belong to the cold type; on the contrary, they were a bit soft and beautiful.

It was just that her usual expression was always indifferent and cold, easily making people feel a sense of distance.

However, it was completely different when she was with him, occasionally still a "ying-ying" monster.

The two were pressed tightly together, and they could hear her panting between words.

Song Yao turned back and glared at Xu Qingzhou, only to see Xu Qingzhou looking at her calmly and innocently. She thought to herself that this guy's skin was thick. Alright, she seriously suspected this guy wasn't asking at all.

He just wanted to experience the feeling of teasing her, this Song Laoshi.

Can't be shy, otherwise this person would be even more proud.

Song Yao said coldly: "Here, adjust the formula for market risk price to be consistent with risk-neutral pricing."

Xu Qingzhou was listening, his right hand holding a pen, recording what Song Yao just said in his notebook, but he wasn't listening that carefully, one hand wandering in front of the school beauty's chest.

After a long time.

Song Yao slapped Xu Qingzhou's claws away with a "pia" and gritted her teeth, "Xu Qingzhou, are you asking a question!"

"You don't think I'm helping for free, do you?"

Xu Qingzhou said as a matter of course.

"Get up, I'm not explaining anymore."

Song Yao got up from Xu Qingzhou, her snow-white cheeks flushed with a heart-moving redness.

"Alright, I'll explore it myself."

Xu Qingzhou was not satisfied, just wanting to see the school beauty's enduring expression, and couldn't help but smell his fingertips.

This action made Song Yao grit her teeth in anger, and she returned with her fist clenched.

Bang~

After giving this hand-itchy guy a few punches, Song Yao happily went to take a shower.

"Together?"

"You're dead if you dare to come in." The school beauty's voice came from the bathroom.

Xu Qingzhou curled his lips, thinking to himself that he really wanted to try, but noticed Wang Xiaping sent a message saying she was going to call, so he dismissed the idea.

Bathroom.

Song Yao pricked up her ears to listen to the movement in the living room, discovering Xu Qingzhou was still lying on the sofa, and muttered in a low voice: "Afraid now, coward."

(End of chapter)