[monte_carlo] Editorial Comments

[HumphreyYang]

Comments by @longye-tian:

Code

• Change global variables to default_param (i.e. default_μ).
• Distinguish the function name in the exercise solution and the one in the main text.

Content

• "we write this statement as" - > "We write this statement as"
• Capitalize only the first bullet point below: "This is the Monte Carlo method, which runs as follows:"
• change another lecture to myst doc link
• "Pricing a european call option under risk neutrality" -> "Pricing a European call option under risk neutrality"
• "Risk-Neutral Pricing" -> "Risk-neutral pricing"
• "$S_0$ is normally distributed" -> "$S_0$ is log-normally distributed"

Comments by @Jiarui-ZH:

Content

• 18.2.2 - look at adding an animation to demonstrate Monte Carlo (similar to Wikipedia page)
• Add explanation for number produced by code above section 18.3
• In 18.3 explain what a European call option is (move definition towards top of section?)
• Add explanatory text at the end of Section 18.3 (to explain number better) -- perhaps relate it to parameters and see how it varies with discount factor, expected payoff goes up (for example)
• what does { mean after 18.4.1 equation? (independent over time sequence)
• In section 18.4.1 and 18.4.3, it would be a good idea to break down the equations in the section and talk about what are the implications behind parameters such as ξ
• Update figures to use mystnb metadata for Figure numbering and titling
• Backstory to Figure above 18.4.6 (why are there two plots?)
• Change section title for 18.4.6 to Computing the option price
• Get more intuiting between prices and parameters

[mmcky]

@Jiarui-ZH would you be able to take on your comments and setup a PR when you have time?