1

Stochastic Calculus Jobs (NOW HIRING)

Director, Model Validation

New York, NY ยท Hybrid

$150K - $261K/yr

Deep knowledge of stochastic calculus, probability theory, and numerical analysis. * Strong programming skills in C++ and Python; experience with distributed computing a plus. * Verbal & written ...

Strong foundations in stochastic calculus, risk-neutral pricing and Greeks. * Knowledge of numerical solvers like Monte Carlo simulation (ideally including American Monte-Carlo) and PDE methods ...

Strong foundation in advanced mathematics and statistics, including probability theory, stochastic calculus, numerical methods, and linear algebra * Experience with data analytic tools such as SQL ...

next page

Showing results 1-20

Stochastic Calculus information

See salary details

$11

$25

$43

How much do stochastic calculus jobs pay per hour?

As of Jul 8, 2026, the average hourly pay for stochastic calculus in the United States is $25.08, according to ZipRecruiter salary data. Most workers in this role earn between $17.31 and $28.61 per hour, depending on experience, location, and employer.

What are the common challenges faced by professionals working in stochastic calculus roles?

Professionals working with stochastic calculus often encounter challenges such as interpreting complex mathematical models, ensuring numerical stability in simulations, and translating theoretical results into practical applications. Given the abstract nature of stochastic processes, effective communication with colleagues from non-mathematical backgrounds can also be demanding. Additionally, staying up-to-date with new research and computational tools is essential, as the field constantly evolves, especially in finance and data science settings.

What is the difference between Stochastic Calculus vs Quantitative Analyst?

AspectStochastic CalculusQuantitative Analyst
Required CredentialsMathematics, Statistics, or Financial Engineering degreesMathematics, Statistics, Finance, or Economics degrees
Work EnvironmentResearch, modeling, and theoretical analysis in finance or engineeringDeveloping models, analyzing data, and supporting trading strategies
Industry UsageFinancial institutions, risk management, derivatives pricingInvestment banks, hedge funds, asset management firms

Stochastic Calculus focuses on the mathematical tools used to model randomness and uncertainty, essential for pricing derivatives and risk assessment. Quantitative Analysts apply these mathematical techniques, including stochastic calculus, to develop financial models, analyze markets, and inform trading decisions. While stochastic calculus provides the theoretical foundation, Quantitative Analysts utilize these methods in practical, industry-specific contexts.

What is stochastic calculus and what is it used for?

Stochastic calculus is a branch of mathematics that deals with integrating and differentiating functions that involve randomness, typically modeled by stochastic processes such as Brownian motion. It provides the mathematical foundation for modeling systems that evolve over time with inherent uncertainty, such as stock prices, interest rates, and physical processes influenced by random noise. Stochastic calculus is widely used in quantitative finance, engineering, physics, and other disciplines to analyze and predict dynamic systems where randomness plays a key role.

What are the key skills and qualifications needed to thrive as a professional specializing in stochastic calculus, and why are they important?

To excel in a role focused on stochastic calculus, you need advanced mathematical knowledge, particularly in probability theory, differential equations, and stochastic processes, usually supported by at least a master's or PhD in mathematics, statistics, or a related field. Familiarity with computational tools like MATLAB, Python (with libraries such as NumPy and SciPy), and specialized statistical software is typically required. Strong analytical thinking, problem-solving abilities, and attention to detail distinguish top professionals in this area. These skills are critical for accurately modeling and analyzing random systems, which underpin decision-making in finance, engineering, and scientific research.
More about Stochastic Calculus jobs
Infographic showing various Stochastic Calculus job openings in the United States as of July 2026, with employment types broken down into 71% Full Time, and 29% Part Time. Highlights an 75% Physical, and 25% Remote job distribution, with an average salary of $52,166 per year, or $25.1 per hour.

Director, Model Validation

BMO Capital Markets

New York, NY โ€ข Hybrid

$150K - $261K/yr

Full-time

Medical, Life, Retirement

This job post hasย expired 1 day ago.ย Applications are no longer accepted.


Job description

Application Deadline:

Address:

151 W 42nd Street

Job Family Group:

Audit, Risk & Compliance

Performs validation of models and assesses model risk to confirm model appropriateness and capability for a designated portfolio. Provides effective challenge during model development and communicates decisions regarding model use to the business/management to ensure transparency and understanding of models and model risks. Assesses model's capabilities, stress points and limitations; assesses the associated model risk and the controls in place to mitigate identified risks.

Teams and Culture:

  • Fosters a culture aligned to BMO purpose, values and strategy and role models BMO values and behaviours in all that they do.
  • Ensures alignment between values and behaviour that fosters diversity and inclusion.
  • Regularly connects work to BMO's purpose, sets inspirational goals, defines clear expected outcomes, and ensures clear accountability for follow through.
  • Builds interdependent teams that collaborate across functional and operating groups to create the highest value for all stakeholders.
  • Improves team performance, recognizes and rewards performance, coaches employees, supports their development, and manages poor performance.

Key Responsibilities:

  • Develops validation strategies and plans to ensure appropriate type and level of validation of models is carried out.
  • Independently validates / tests models and their associated assumptions, benchmarks, and supporting documentation against model validation process, standards, guidelines and principles, which includes:
    • Lead model validation efforts across various volatility regimes, including stochastic volatility, stochastic-local volatility, and jumpdiffusion frameworks.
    • Develop, enhance, and maintain independent benchmark models for exotic derivatives (e.g., autocallables, barriers, quantos, range accrual, variance products, hybrids).
    • Analyze complex payoff structures and produce accurate pricing, Greeks, and scenario analyses.
    • Review and validate model calibration routines to vol surfaces, correlation structures, and multiasset dynamics, and assess the data for model development as well as inputs to the model;
    • Design and implement scalable testing libraries using C++, Python, or similar highperformance languages.
    • Compares validation results with model developer results for replicability.
    • Measures the effectiveness of validation and monitoring framework; recommends changes as required.
    • Identifies deficiencies, conditions for model use, recommends changes, and escalates as required; quantifies model risks, documents outcomes and communicates with stakeholders. (detailed work)
    • Identifies where corrective actions are required and escalates per guidelines; monitors and ensures corrective action is taken.
  • Optimize numerical methods (e.g., PDE solvers, Monte Carlo engines, adjoint methods) to improve performance and stability.
  • Coordinates and monitors the review and sign-off of model validation reporting including model inventory and model inventory attestations.
  • Mentor junior quants and contribute to longterm quantitative research initiatives.
  • Collaborate closely with trading desks to deliver strategic analytics, improve risk metrics, and support trade ideation.
  • Provides technical advice and guidance to assigned business/group on implementation of the model validation framework, and resolution of model risk issues.
  • Makes recommendations to senior leaders on strategy and new initiatives, based on an in-depth understanding of the business/group.
  • Represents the model validation program / portfolio for internal/external regulatory audits and/or examinations.

Qualifications

  • Advanced degree (PhD or Master's) in quantitative fields such as mathematics, financial engineering, physics, or computer science.
  • 15+ years of handson experience in equity derivatives model validation or frontoffice quantitative research.
  • Deep knowledge of stochastic calculus, probability theory, and numerical analysis.
  • Strong programming skills in C++ and Python; experience with distributed computing a plus.
  • Verbal & written communication skills - In-depth / Expert.
  • Analytical and problem solving skills - In-depth / Expert.
  • Familiarity with regulatory frameworks (e.g., FRTB, model risk governance) in a derivatives context.

Salary:

$150,700.00 - $261,800.00

Pay Type:

Salaried

The above represents BMO Financial Group's pay range and type.

Salaries will vary based on factors such as location, skills, experience, education, and qualifications for the role, and may include a commission structure. Salaries for part-time roles will be pro-rated based on number of hours regularly worked. For commission roles, the salary listed above represents BMO Financial Group's expected target for the first year in this position.

BMO Financial Group's total compensation package will vary based on the pay type of the position and may include performance-based incentives, discretionary bonuses, as well as other perks and rewards. BMO also offers health insurance, tuition reimbursement, accident and life insurance, and retirement savings plans. To view more details of our benefits, please visit:https://jobs.bmo.com/global/en/Total-Rewards

About Us

At BMO we are driven by a shared Purpose: Boldly Grow the Good in business and life. It calls on us to create lasting, positive change for our customers, our communities and our people. By working together, innovating and pushing boundaries, we transform lives and businesses, and power economic growth around the world.

As a member of the BMO team you are valued, respected and heard, and you have more ways to grow and make an impact. We strive to help you make an impact from day one - for yourself and our customers. We'll support you with the tools and resources you need to reach new milestones, as you help our customers reach theirs. From in-depth training and coaching, to manager support and network-building opportunities, we'll help you gain valuable experience, and broaden your skillset.

To find out more visit us at http://jobs.bmo.com/us/en

BMO is proud to be an equal employment opportunity employer. We evaluate applicants without regard to race, religion, color, national origin, sex (including pregnancy, childbirth, or related medical conditions), sexual orientation, gender identity, gender expression, transgender status, sexual stereotypes, age, status as a protected veteran, status as an individual with a disability, or any other legally protected characteristics. We also consider applicants with criminal histories, consistent with applicable federal, state and local law.

BMO is committed to working with and providing reasonable accommodations to individuals with disabilities. If you need a reasonable accommodation because of a disability for any part of the employment process, please send an e-mail to BMOCareers.Support@bmo.com and let us know the nature of your request and your contact information.

Note to Recruiters: BMO does not accept unsolicited resumes from any source other than directly from a candidate. Any unsolicited resumes sent to BMO, directly or indirectly, will be considered BMO property. BMO will not pay a fee for any placement resulting from the receipt of an unsolicited resume. A recruiting agency must first have a valid, written and fully executed agency agreement contract for service to submit resumes.